My lvl 3 Oath of Redemption Tiefling Paladin and her crew are set to level up soon, and I've been eyeing some feats for her to take on. I'm pretty brand new to the game, so I'm not sure what feats are actually useful or viable for paladins in general. My girl is, technically speaking, the "tank" of the group. Besides the cleric, everyone else are pretty much squishy spellcasters. And the bard. Last combat encounter we had was ABSOLUTELY BRUTAL and my paladin nearly biffed it. What I'm looking for in a feat is damage output or protection... But mainly damage output. Magic Initiate sounds interesting lore-wise, plus I would love to have some cantrips to fall back on when all my spell slots are used up. But other feats, such as Sentinel, sound like they might be more viable when keeping the party build in mind. Any thoughts or advice on the matter?

Heavy armor master will increase your tankiness.

Polearm master will increase you DPS.

Sentinel will help protect your party.

Magic initiate will increase your versatility (grab a ranged cantrip for example).

which type of tiefling are you using?  If you had the option many of the subtypes of tiefling have combat cantrips, otherwise I don't think I would recommend the Magic initiate unless there is a level 1 spell you desperately want access to.  most circumstances having thrown weapons should get you through scenarios where you can't get up close and personal.  In addition there is nothing wrong with taking a defensive action like Dodge or using Help to assist a teammate.  

Shield Master can be useful if you are using a one handed weapon.  A little bit of versatility and the ability to avoid some damage from dex based saves.

Base game vanilla tiefling, unfortunately. Shield Master would've been an good choice, but sadly would kinda clash with her Great Weapon fighting style. And the fact that she currently has no shield, so to speak...

Heavy Armor Mastery or whatever it is called would be an option for some damage reduction as well.

You may also consider flames of phlegethos, but that would be better with more fire cantrips like firebolt or green-flame blade.

It might be less sexy, but if you want to be as effective as possible I would concentrate on ASIs.  A paladin needs a high score in strength (unless you are dex based), charisma and constitution. (and wis and Dec are important enough that completely dumping them can cause problems)

Increasing strength will improve your damage and for most builds would be what to improve first.

Even if you use all you spell slots for divine smite, Increasing charisma increases the power of turn unholy, and if you are oath of devotion you sacred weapon. When you hit level 6 Aura of protection is a great cha dependent buff.  If your campaign is the type where you often only have one fight a day and / or you like to cast cha dependent spells you might want to up that first.

Increasing con improves your tankiness , though it is probably your 3rd stat, if you con is odd and one of cha and str is odd it might make sense to AS I both of them. 

Sentinel is, imo, obligatory for any tank that doesn't have alternative lockdown/stickiness options.  Ie, a conquest paladin can arguably get away without it, but imo every other paladin that wants to focus on tanking should take sentinel as their first asi.

Beyond that, paladin is very stat intensive, between strength or dex as a primary attack stat, charisma as a strong secondary stat (or even co-primary for oath of conquest), and constitution likewise being very important given paladin is both a melee tank and a concentration caster.

As such, you're almost always better off taking stat bonuses instead of feats.  between sentinel, max strength, and max charisma, most paladins won't even have leftover space for feats.

If you're building for damage above all else the feats like PAM or GWM will do more for you than raising Cha, but imo that's missing out on some of the better parts of paladin to do stuff that regular fighters can do better.

Sentinel seemed a pretty obvious choice from the get-go, but it's good to have confirmation! Luckily, our DM allows us to take on our two ASIs and a feat, so it's not like I'd be choosing between vital stat improvement or feats.

Bless yourself or have the cleric use and choose great weapon master. Damage doesn't get better then that. 

 Inspiring leader is a solid utility feat to make your party less squishy. It also can have some fun role play as you rally the party to your redemption cause every chance you get.

Dont know what your stats are but if you have at minimum a 14str I wouldn't worry to much about strength. Yes a paladin needs strength. I'm not saying they dont, however, there are plenty of items that increase your strength to just under or well above 20str. There are not alot of items that increase chr or con. If using ASIs I'd focus on raising those not str.

This said if you're a great weapon paladin your first feat hands down should be Great Weapon Master or polearm master if you're using polearms. You're next could be sentinel if that's what you want.

Agree with KhaldoDraigo - unless you think your DM feels otherwise - you are likely on your way to some sort of magical strength buff. I wasted one of my ASI moments because 2 adventures later I came up with an item that took me to strength 19. 

I know you want damage but paladins also benefit from going first. with my oath of vengence  + Alert feat - I could rush up to a target first, throw an oath to get advantage, and crack the bad guy with great weapon (-5, +10) and add in divine smite. you will be quickly approaching 40-ish damage depending upon your stats and the level spell you used to divine smite.

And if you crit...