To get them working together, I would start with an old-fashioned dungeon crawl, with the dead-inside one working for the main villain and under orders (on pain of death, of course) to monitor and subtly sabotage the rest of the party (as part of the villain's scheme to protect themselves from heroes). 

• The combat-obsessed one gets to kill lots of monsters and take their stuff. 
• The noncombatant gets to talk the monsters into joining the party temporarily, which the combat-obsessed one will probably appreciate, because it gives them minions (have the combat-focused player run the minions, but remember that they probably won't be willing to go on suicide missions). Later on, the noncombatant gets to figure out how to deal with the villain. 
• The other one has a reason to work with the party, but still gets to do what they enjoy.  The noncombatant will possibly enjoy the traitor's eventual dramatic reveal, which will give the combatant an interesting fight. 

Quote from ADrunkenDwarf >>

Hi All! I'm new to the world of DMing and I'm already blatantly terrified of how to start. I've seen how my players operate already, and let's just say it's a bit worrying. One's only interested in combat, One always looks for a non-combat solution and is invested in politics, and one seems totally dead inside but willing to sacrifice any NPC or PC he comes across, killing themselves and creating a new them every 5 minutes. As of such, I'm going to have to come up with something good to begin with to engage them all. I've created a massive Homebrew world, but I'm not sure where to put them to begin with. If it goes wrong they're going to end up warring with each other.

What's the main way you guys start off a Campaign with new Players/Characters? And any hints to anything extra cool I can do?

Oh, and does your Campaign usually center around a main Narrative (think Alduin and Skyrim) or is it more 'side quests'(any other Skyrim quests)? I have a great Narrative planned out but I'm scared that once it''s done the players will lose interest in the rest of the world.

 
I am wondering how long you have played together?  How do sessions normally go?  You know what to expect better than any of us but do not confuse what will probably happen for trepidation at starting your own adventure.  If your group normally gets along well then things will be just fine, I am sure.

I once started all of the players in a shared vision where they were facing a low level baddy that would be introduced in the coming sessions.  They all awoke from the vision when a wise looking older man told them to find him in xxx place to avoid the bad things they had just seen.  As they arrived in town, one by one, not knowing each other they recognized each other and began to get to know each other until the looked around town for a day or two and found the old man.  I have not yet tried "You all wake up in a close confined space.  You push up to find the surface above you hard but yielding.  A flat door opens and you sit up to realize that you all are in coffins..."

As to main narrative or side quests, a good mixture of both.  You have the main direction for the campaign but it needs to have the side quests so that the players feel like they have a choice as to where the party will go.  And a fine line lies between a sandbox and a railroad and with time you will learn how to balance it.  All you need to get started is the beginning location, populate it with people and a few items per location.  Fix two side quests and a main quest for the area.  Have a couple of general encounters ready to go at a moments notice.

AND HAVE FUN!  You bring the best world you can and let them tell the story.  Hopefully they will play nice.  If so, only awesomeness will ensue and you all will be the better for it.

Whenever I start a new campaign, I always give the adventures a chance to introduce themselves to each other then throw a major baddie at "them" to show the the BBEG (or, at least, some of his minions).

For instance, at the start of my last campaign, I had the adventures meet in a tavern and they got into a bit of a bar brawl (monk's fault). In the middle of the night though, they awoke to find a Dragon attacking the town. PCs with Draconic would hear the Dragon asking for "it" to be returned (with "it" being intentional vague). After saving some villagers from the rampage and engaging it atop the local castle walls with the castle guards, one of the PCs notice the Dragon's iris suddenly shrink before the Dragon ceases the assault and flies off.

Utter confused by the events, the PCs are now convinced that something larger is afoot and take off to search for this Dragon to stop his rampage.

 I have a great Narrative planned out 

In my opinion,  don't do that :)    

Perhaps create a set of short story/ideas that could form a trellis, but the actions of the PCs should create the story.

I recommend starting small, perhaps with a minor town or encounter.  You need a quick initial conflict to help bring the party together (unless you are doing this with backstory), but even then -- initial conflict helps forge bonds.

Back to the narrative discussion,  define the motivations for your BBEG and your NPCs then let things grow organically from there.

Just my opinion, and all gaming tables are different, so I hope some of the above helped :)

I figure the players need to tell you how they came to be in one place at this time.

Second, the players and the DM need to decide why the party became a coherent group.  Did they meet at an Inn in response to some ad?  Were they brought together by some individual advising them they would want to band together?

For the reasons that the party came to this place on their own, you (the DM) should be able to work out the political, economical and social fabric of the locale, even though it doesn't have to be a settlement where they meet face-to-face.  But the players would have some reasonable knowledge of the society so they should have that from the DM.  Then they should have to decide whether to abide by local customs or not, and possibly suffer the consequences.

Once the players and DM decide why they came to be in this place to meet, then the DM needs to provide information that leads to an adventure.

In my opinion, that is how to begin a coherent story.

Now there are some ways to shortcut this.  The players could be prisoners and have been brought there.  And the place they are in may be quite unfamiliar to them.  But then a coherent story needs to be built around that.  The players could be shipwrecked.  They were all on the same ship, but they were headed in different directions when they got to the other end of the sea journey.  Some may have been going somewhere else, and some may have been going home.  But now they are shipwrecked in an unfamiliar place.  They probably decide they need to stick together until they reach civilization again.  Now the DM has an almost unlimited choice of how to proceed.

Good luck.

So far I have used 2 starting points, a one shot that went with the Elder Scrolls tradition of you are locked up somewhere, the whole session was then get through the wizards tower and escape. The other start I have used for a few different groups now as either a 1 shot or opening a campaign. The party are traveling with some merchants (each can make up their own reason why) then the village they are approaching is attacked, they are then encouraged to go track down the source of the attack the next day. The main thing about your opening is that there needs to be some issue and a clear way for the party to set about resolving it in order to quickly get into things, you can always open it up and give them greater flexibility once everyone is a bit settled.

I also second Koradgees comment about the narrative, if you want to have a well laid out series of events then write a book/film/video game, with a tabletop game there are so many more options available that attempting to stick to a well orchestrated narrative will either end up with you lost when the players go off script, or the players notice you are pushing everything in very specific directions and will probably lose interest. Having a general idea of how things might develop is fine, but you also need to be prepared to adjust to the players doing all manner of unexpected things. Rather than planning out a detailed series of events you are better off getting into the mind of the BBEG, establishing motivations and resources, then whatever the party get up to you are more likely to be able to adjust on the fly and keep things going. Although any big set pieces you have come up with as part of your narrative can be sprinkle in throughout or saved for other campaigns so that effort is not wasted.

A relevant example, my 2nd session was supposed to include clearing out a load of goblins that had mined into the taverns cellar, I had initially planned to have the goblins start raiding the town if the party ignored them. But after finding out it was goblins, the party ran off to find a translator that could speak goblin and ended up getting the goblins and the city together to negotiate a trade deal. Now the party are Lv6 and have just tied up a short arc to get all of us settled in, so a new big bad is creeping out of the underdark and some missing goblins was the first indicator that something is wrong.

I have come to skip the standard "you are all in a tavern when..." opening. 

I ask the players during character generation to tell me what sort of adventures they are excited about with these characters and to talk with each other about what sort of characters they are making and why they are together.  Often this is met with the chirps of crickets and a misfit bunch who hold together about as well as dry sand.

I usually start the game with some clear adventure hook dancing in front of the characters. Aunt Lucy has gone missing and you have been hired to find her. The old house on the edge of town is said to be hasted, there is a reward for anyone who can get to the bottom of what is going on and clear the spooks out. Goblins attacked a merchant a day's travel from town. How they decide to tackle it is up to them.

I also try to have several potentially interesting things going on around the initial starting area. that way if they don't bite on one adventure hook I have a couple more baited and ready. For larger campaign threats and Big Bads I try to think of a couple of ways they could become involved. 

I have had players completely throw me for a loop and set off on a wild chase across the campaign world with designs of their own.  When this happens I just try to get ahead of them if I can. But these can be the best campaigns because I know it is something the players are interested in and excited about.  It is why I tend to prepare worlds and settings more than stories in those settings. Lord Farquad doesn't like his neighbor has the potential to go in a lot of directions. Lord Farquad hires the PCs to kidnap his neigbor's daughter, then the neighbor send s a mage to get her back from the players, when they discover the Gem of Don-Ki, after which... depends on things going just so. The whole story goes off the rails if the players decide they don't like Lord Farquad and refuse to work for him.

"- one seems totally dead inside but willing to sacrifice any NPC or PC he comes across, killing themselves and creating a new them every 5 minutes."

I don't think I have ever seen such a keen, succinct, or tame explanation of a murder hobo that didn't have a single expletive in it... Kudos.

1: that's rough buddy

But 2:  don't try to change their play style unless they start hindering or, heaven forbid, eliminating someone else's fun. People will play how they would like to, even if they are less active in RP and conversation. They'll even say "This is fun". But feel free to give the party a pep talk ahead of time and just say something to the effect of,

"Improvisation games like this depend on character's saying, " Yes, And" not, "no, But"."

That they will all get what they want to do in equal terms and due time if they practice patience, and participate. They may even find new ways to have fun playing it, even as veterans.

For the murder hobo though... I'd tell them to calm down. No threats, no punishments, just let what happens happen and ask them to dialback a bit... Outside of booting, them which you really shouldn't do, there's not a whole lot that can be effective. Just thank the mighty d&d lords that they aren't an incendiary troll that goes out of their way to break the game.