Generally, my experience is that when you hit a brick wall you want to grind up some gold and heirlooms with your Levels 0, 1, and 2 groups so that you can afford to fully kit out your Level 3+ ones with upgrades. Proper armor, weapons, and techniques make for a very solid party even without clever strategies. And good strategies have let me level dudes entirely sans upgrades up to around level 3 or 4, depending on how forgetful I get. I don't think they should put that advice in one of the loading screens, though - that sort of thing is the kind of thing that's intuitive enough to let people discover it. It'd be almost like telling people that a Plague Doctor works well with an Occultist because she can stop bleeding.
Also, pro tip: fight bosses at the maximum level the game will let you. So Level 2 for Tier 1, Level 4 for Tier 2. Tier 3 doesn't matter so much since there are no upgrades to be purchased at level 6, but IIRC you still get a bit of an edge in resistances and so might as well wait.
Also, think about party composition. My rule of thumb is to always have 1 healer, 1 "support" character, and 1 brute force attacker. Last one is a wild card, filled with whoever's convenient or happens to work nicely with the rest. Support, for me, means a character that enhances others but isn't great alone - a Plague Doctor setting Blight or Stun, or a Man-at-Arms providing buffs, or a Houndmaster managing group stress or setting bleed as situations call for it. They tend to fit well into any party, but some cute synergies can be useful (a Man-at-Arms can use Rampart to stun things while pushing a Crusader back far enough to use Holy Lance, for example). Try to make sure at least one, preferably two, have access to a self-moving ability to help keep you from spending a ton of dead turns if folks get pushed around.
I really like what Early Access has done for the game, actually. I've got a sense that many games use it as a means to charge for an unfinished product, but in this case they've used it effectively as a mechanism for getting feedback as development proceeds.