There's not a lot you can do within the stripped down BB rules, since there just aren't many options to pick from, but in general stuff that's strong in core is still strong in BB.
Clerics don't really have much in the way of options. Probably the best option is to take the superior powers offered by Desna, pump strength, and be a classic front-liner cleric with a toolbelt of defensive and support spells. There's not much else you can do. There aren't many spells that call for saving throws on this list, so you can skimp on wisdom easily. Make sure you've got at least 13 in wisdom then balance the points elsewhere as desired. Go with either heavy mace + light shield or spend a feat on greatsword proficiency.
Two-handed weapon fighters are virtually unaffected by the limitations of beginner box, since Power Attack is unchanged and that's pretty much the only feat they need. You don't have access to any reach weapons, but that's not a huge loss. It looks like composite longbows and the rapid shot feat don't exist in BB, so archery looks like a questionable route.
The Rogue is pretty bad in core, but it does have a niche in BB because literally every other class in BB is terrible with skills. Now there's really nothing in BB to make dexterity-based fighting effective, so I would say to go strength-based. Spend a feat on proficiency with something like a greatsword and basically play like a Fighter who is slightly less accurate but gets sneak attacks. You'll need to run some dexterity since you're locked into light armor. It's a shame that multiclassing isn't a thing, because Fighter/Rogue looks really good under BB rules since Evasion works in medium and heavy armor.
Interestingly a number of things for the Wizard are actually better than they are in the full version of the game. Hand of the Apprentice is a much stronger ability, and for spells Sleep, Hideous Laughter, Stinking Cloud, and Clairvoyance are all better than they are (and Sleep and Stinking Cloud are pretty great as it stands). Meanwhile Haste, Fly, Web, Invisibility, and Charm Person are on the list virtually unchanged. This is more than enough to fill out your daily spell loadout with great options. The specialist schools are significantly less attractive than in core and I'd definitely go with universalist.