Hey guys, so i have never posted here before so if i'm in the wrong place for this please tell me.

So im starting at 5th level in a new campaign and my gm wont tell me what the other players are playing, he just told me to "built what you want to play and the others can build around you." probably because i have a bad habit of trying to fill too many roles at once when our party doesn't want to focus on any particular job with their own builds. So, i decided "alright yea! I wanna play a paladin, I haven't played one since pathfinder! I know that i want to be our big tanky girl but id like to focus on sword and board, very big ac, and plenty of melee damage. Im not concerned with doing much else. I know ill have the skills and stats to be a face if required but im planning to play the stoic type so that even though i CAN be the party face, someone else can happily take that role. We are point buy and this is my build so far. 

Fallen Aasimar, level 5 Oath of Vengeance Paladin

Str: 16 (15+1)
Dex: 10
Con: 14
Int: 8
Wis: 10
Cha: 16 (14+2)

Fighting style: Protection/ defense/ dueling 
4th level: (Feat) Sentinel/War caster/Resilient(con)

So this is the plan, im afraid my gm said that even for 5th level adventurers we are starting with level 1 starting equipment.....so no chance of any gold to buy stuff or any proper armor for my level yet....and i asked him about the shield master feat and he said that i have to use all my attacks first before using its bonus action shove so its basically worthless to me now so its not an option otherwise it would be the obvious feat choice. What do you guys think? What combination of fighting style and feat can i take to make sure i can be tanky AND deal plenty of damage? 

I'm not a fan of protection fighting style, I think either defense or dueling would be much better. If you're going shield and sword and not polearms or 2Hs,  I'd say Dueling is the way to go. Sentinel is probably the best tanking feat, although it can be limited to 1 enemy per turn.

Dueling/Sentinel Paladin with Sword/Shield should be welcome in any party.

On a side note, as a sheer tanky damage dealer you'll naturally be outshined by a barbarian's overall bulk, so you'll have to use your spellcasting/smites/auras to be a good paladin.

Im not especially concerned as i know the people im partying with at least and know that the likeliness of them playing a barbarian is pretty close to zero. Though ill take the advice, dueling and the sentinel feat. Should i be concerned about concentration checks? I only have plus 2 to my con checks for now, though next level ill have plus 5 to them via my level 6 aura. I know my vengeance spells use a decent amount of con checks when i take a hit and ill be using hunters mark a whole lot. 

You bring up a good point with the CON saves. Let's just make this clear that I've personally never played a Ven. Paladin, I do know you guys get haste at 9, which is pretty badass. But losing your CON save on haste is not so badass. I personally wouldn't sweat a lvl 1 hunter's mark, but haste can be a different story, and you know to each his/her own, I'm just putting out my own 2 cents

You probably already know you'll get +5 to save @ lvl 6 so it's really up to you. If you have a dedicated Bless Bot cleric, it'll also change things. You also might have mapped out a generic sense of what ASI's or feats you're going to get, and it's freaking chore as a paladin, no matter what you'll be short on one or two things.

My sole advice is to pick a strong point you really enjoy and stick to it, and let magic items supplement your weakness. I know it's dumb, but I really like the level 6 aura of paladins, so I always try to max out my CHA. It's not ideal in many cases, but there might be a Hill Giant Belt or Amulets of Vitality or Cloaks of Protection somewhere along the way (Of course, it's no guarantee...)

I hope you are right though from the other campaign ive played with this gm ive learned that he is SUPER stingy with rewarding gold and magical items, he doesnt like to use them much if he doesnt have to or he likes to award them at the very end of like huge, massive stuff. We didnt get a real piece of magic equipment until the end of our lvl 1-5 campaign last time, then we got kitted out for the final boss and that was about it. A few extremely minor or 1 use items until that point. 

Just asking out of curiosity, why Vengeance Paladin? What is it that you like about it?

Its capability for damage, its dedication to justice and defending whats "right", all of its bonus spells it gets are just amazing, a decent chunk of them being bonus actions is really really cool, the flavor of the big paladin that obliterates evil and specializes in big bad guy killing is kind of super exciting to me. 

Seven months ago, this was posted, but if I wanted to build a tank, I would probably go Oath of Ancients - for the spell resistance aura later and dueling fighting style for a sword and shield (+2 damage with a 1h gives you 3-10 damage with a longsword i.e. average 6.5, which is as much as the damage from a 2h great axe, but you still have a shield).  

Stats look fine. If you want to tank remember that your main job is to maintain the enemies attention and to soak damage (via your high armor and hit points) that would probably kill less robust characters.

Take the Defense fighting style - bounded accuracy makes this more useful for a tank profile and paladins do most of their damage through smites anyways so the extra dueling damage isn’t as vital. 
If you want a feat, then take sentinel. It’s the only one that will help you keep an enemies attention on you. But you would be better off putting 2 points into strength. It’s a greater benefit to your Paladin at your level and with basic starting equipment. 

This video goes into a bit more detail if you are looking advice to get you started.