Originally, I was thinking the short list had to be Fighter, Barbarian, and Paladin...but really if we're restricted to exclusively 1st level in 5.5e, it's got to be Fighter.
Barbarian's only durability boosters at 1st level are that it resists B/P/S damage while raging, and it has +2 bonus hit points. But now that Rage doesn't play nice with heavy armor, you're practically guaranteed to have worse AC, and you have no ways to heal yourself outside of Hit Dice...which only on average give you +1 HP compared to the d10s that Paladins and Fighters use. So Barbarian is pretty well out--you do take less damage, but once you're out of those HP, you're out.
Paladin is a tricky beast because I think some folks forget that it can now cast two 1st level spells at character level 1. That's a pretty stark change from 5.0. It means the 5.5e Paladin can now top herself up with two uses of 2d8+CHA healing (assume 2d8+2, if Str and Con are getting the 16s), for an expected average of +11 HP per use--which is going to be nearly a full self-heal! And then they also get 5 points from Lay on Hands. So that's an approximate average of +27 HP/day.
The Fighter, meanwhile, has Second Wind, and gets slightly more uses than 5.0 did; you now start with two and get one back per short rest. Ironically, by being smaller and swingier, this is actually somewhat more useful than the spells above; at 6.5 average HP per use, you're getting enough benefit to make it worthwhile, but not so much that you'll be afraid to use it unless you're getting full efficiency out of it. At higher levels, when there are more HP to lose, the Paladin would pull ahead even for unchanging amounts of healing. The sticker is in the need for short rests: the Fighter is stuck with only 13 HP/day if they never get any short rests, not even half the Paladin. They absolutely must get at least two short rests in order to even keep pace (6.5 x 4 = 26), though efficiency is a valid concern--but by that same token, those 5 points from LoH are perfectly efficient, while SW may still overheal, just with less chance than cure wounds.
So:
If you know your group takes the actually expected number of short rests (2-3) per day, then Fighter. If you are pretty confident you aren't going to get 2 short rests per adventuring day, Paladin.