Mechanically though, they're tricky, because they're kinda anti-synergistic and none of their individual abilities are really stellar. Their natural armor doesn't do anything unless it's on a Dex build (or perhaps someone who would otherwise have no armor at all, like a Wizard), and won't work with Barbarians or Monks. Their natural weapons and Hungry Jaws want you to make Strength-based attacks (and use Constitution for the number of temp hp). And their statline has neither Dex nor Strength nor a casting stat for unarmored casters. And they don't have Darkvision.
As you can see, they're kind of all over the place. You generally benefit from Natural Armor OR Hungry Jaws OR fit snugly with their stat typing... but only one of those. And the rest of their abilities are just skill proficiencies and ribbons. I guess you could maybe argue that Hungry Jaws can be used to chow down on things out of combat (and thus not care about Strength), but some DMs might get gamey and say that you can only engage in a feeding frenzy "in battle" due to the first line of the ability. On the other hand, carrying around a live chicken to devour does seem like a rather Lizardfolky thing to do.
So we want a non-caster, that minimizes our MADness, and benefits from our racial features.
For a Barbarian, Ancestral Guardian or Zealot could be a decent choice. Both subclasses lack bonus actions, and have abilities that enjoy having the occasional extra attack from Hungry Jaws (e.g. you want to make sure their level 3 abilities proc). Also, a grappler Barbarian will appreciate the ability to attack (via bite) while wielding a shield and holding a foe down. Unfortunately your natural armor won't be doing you any favors. The main concern will be that you have to wait all the way until level 12 to max your Strength, and that's if you don't get any full feats at all before that point. The only half-feat worth considering for +1 Strength would be Tavern Brawler. Alternatively you could start with 15 Str / 17 Con and get a +1/+1 ASI. Whatever way you slice it, your main schtick will be to shove people prone and grapple them so that they can't go anywhere, then bite away despite having your hands full.
For a Dex Fighter, the extra ASIs mean that you can potentially max your stat as early as level 8. Your Natural Armor will allow you to have +1 AC over mundane half-plate while retaining your full stealth ability... almost like you took the Medium Armor Master feat. Hungry Jaws can still give you a few extra hit points from disabled foes or the like. You can start with 13 Str / 15 Dex / 16 Con / 14 Wis, get +1 Str/Dex on your first ASI, and have an at least half-decent bonus action attack 1/SR. Max out your Dex by level 8, and sneak around trying to ambush people with your good Stealth. Go Battlemaster and use a rapier.
PS: I found this thing, which you might find helpful: https://www.reddit.com/r/3d6/comment...folk_handbook/