relatively new to DnD  and about to start off on my first extended homebrew campaign. Party so far consist of a Battlemaster fighter, a trickster cleric, a lore bard, and a Druid. I kind of wanna take on the front line support/tank of the party and I’m torn between Tempest cleric or Ancients paladin. 

What Are the pros and cons of each? Can a tempest cleric do just fine on the front line? Any advice will help!

So you want to be able to dish out damage as well provide some buffs or healing as needed? from what you said about your current party they seem to be lacking a scrapper and more potent arcane powerhouse. How many people are in the party total or this all of them? There are alot of way you can go about being a support/tank and from I what of the party they also lack a barbarian as well.

This is all of them. And we are all pretty new to DnD. I know I want to be either a paladin or tempest cleric But don’t know which one to go with. 

Paladin would be the better choice, they can buff, damage deal, damage soak, heal to some degree. They are no longer alignment restricted like they were is prior editions.

The Tenets of the Ancients  are going to your biggest rp issue.

Tenets of the Ancients

The tenets of the Oath of the Ancients have been preserved for uncounted centuries. This oath emphasizes the principles of good above any concerns of law or chaos. Its four central principles are simple.

Kindle the Light. Through your acts of mercy, kindness, and forgiveness, kindle the light of hope in the world, beating back despair.

Shelter the Light. Where there is good, beauty, love, and laughter in the world, stand against the wickedness that would swallow it. Where life flourishes, stand against the forces that would render it barren.

Preserve Your Own Light. Delight in song and laughter, in beauty and art. If you allow the light to die in your own heart, you can't preserve it in the world.

Be the Light. Be a glorious beacon for all who live in despair. Let the light of your joy and courage shine forth in all your deeds.

How are tempest clerics in the front line too? Some of their abilities seem like they can control the field well. 

Tempest Clerics , like some other spellcasters focus on AoE and crowd control rather than pure frontline assault as you want it to be.

Tempest clerics can do fine on the front lines. But for variety and other reasons I'll mention, I recommend paladin.

As an oath of ancients paladin, you will have smites for big damage, healing spells and abilities (mostly touch range), battlefield control spells, and powerful auras that buff you and your fellow frontliners. You may find yourself short on spell slots at times, you can multiclass to fix that if you want.

I'll second that choice on Paladin. Personally I prefer Oath breaker as a starting place and transition to Redemption later on.

I would say play what you really want to play.  I've played both a tempest cleric and a vengeance paladin.  They are both fun to play, but I think I liked playing the paladin more.  If you really want to play as an oath of the ancients I say go for it.  It looks like fun, and despite what Haseo said about the tenets of the ancients making it a rp issue, I think it actually gives you more opportunities for rp than some of the other classes.  In the end, it's your character and you will play it how you want to no matter what other people say, so just go with which ever one you really want to play as and go from there.  There are no wrong choices.

I'm saying the rp issues are going to be with players, but more or less in the overall storyline, how will it affect and grow the character, will there be a point it breaks them? What will they do if they if they end up violating the tenets? How will the other characters in the group respond?

 I played a tempest cleric triton, and it was so boringly overpowered. They could heal very very well, use call lightning, wear good armor to avoid attacks thus helping concentration on call lightning. You can still heal others and use some ranged attacks, from any weapon to add to the list of things they can do. Being a triton was fitting for them, and having fog cloud then wall of water helped even more with avoiding damage and could keep up call lightning. Not to mention upcasting call lightning and the fact it lasts for 100 turns if you don't lose concentration just for 1 spell slot. Inflict wounds is also very strong before you get 2nd level spells. He then could maximize the damage with destructive wrath, so an easy 30 damage without upcasting call lightning, you can then push them away from you by 10 feet. Extra weapon damage when you can wield any weapon is more damage to stack on while controlling call lightning. If they get to actually attack you, just use wrath of the storm, push them away, skedaddle, recast call lightning. Last, but not least, when you're high enough level, you can just fly!

I didn't really like his character, although I prefer being under powered. Other's may like the strength behind it.

Quote from BobobSyxtieNein >>

 I played a tempest cleric triton, and it was so boringly overpowered. They could heal very very well, use call lightning, wear good armor to avoid attacks thus helping concentration on call lightning. You can still heal others and use some ranged attacks, from any weapon to add to the list of things they can do. Being a triton was fitting for them, and having fog cloud then wall of water helped even more with avoiding damage and could keep up call lightning. Not to mention upcasting call lightning and the fact it lasts for 100 turns if you don't lose concentration just for 1 spell slot. Inflict wounds is also very strong before you get 2nd level spells. He then could maximize the damage with destructive wrath, so an easy 30 damage without upcasting call lightning, you can then push them away from you by 10 feet. Extra weapon damage when you can wield any weapon is more damage to stack on while controlling call lightning. If they get to actually attack you, just use wrath of the storm, push them away, skedaddle, recast call lightning. Last, but not least, when you're high enough level, you can just fly!

I didn't really like his character, although I prefer being under powered. Other's may like the strength behind it.

 You can't use fog cloud or wall of water while concentrating on call lightning. And everything you mentioned other than call lightning or and subclass features, a paladin can also do (weapons, armor, healing, spells).

Fog cloud and wall of water aren't concentration so you still can. While you can't use the lightning bolts, the spell still stays up as a very valid attack, with high maximum damage, and rather exceptional average damage. I still think the whole lightning and thunder power buffs are very strong, but paladins do definitely get higher health rolls.

The fact of only using one spell slot is still very good, when it can potentially last the entire battle and then some. Although, I rarely play paladins, this was my first cleric.

Fog Cloud is a concentration spell as are all wall spells except Prismatic Wall and Passwall

Well I can't see the spells list on the site saying it's concentration, but if two people say it's concentration I guess its right.

that little diamond with the "c" besides the duration means concentration.

Oh! I only knew what the ritual one meant. Thanks for that, yeah then, he shouldn't have been able to use those. Good thing that campaign wasn't continued at least.