My top pick would be a rogue, since very few of their class features rely on expendable resources in the first place. My second pick would probably be Barbarian, preferably Dex-based for maximum survivability. d12 hit die and +con to AC will mean a Barbarian will last through a lot even when we’re out of healing. Next would be fighter. Also highly survivable, with more ASI levels and extra attacks than anyone else means high damage output without resource costs. Next choice would be Warlock. Eldritch Blast scales like a fighter’s extra attack and has several invocations that can upgrade it. Pact of the Fiend would be best in this situation for heals on kills. Preferably with the Tome Pact Boon for ritual spells. Fifth pick is a tough call for me, as nothing else stands out to me as particularly suited to this scenario, but I went with Paladin as essentially a budget second fighter. d10 hit die, martial weapons, heavy armor, and extra attack at 5th level will mean even drained of resources, a Paladin will be reasonably tough and do reasonable damage per round.