Are you looking for powder or liquid foundation?
Estee Lauder's "Double Wear" liquid foundation is extremely long lasting. It's pricey compared to drugstore makeup, but I would say it's your best bet! If you go to an Estee Lauder counter, they can make up a free sample for you. This allows you to take it home and try it for a couple days. In fact, most makeup counters do this if you ask, as well as some stores (like Sephora).
As a cheaper alternative, Covergirls Outlast foundation is pretty long wearing, matte, and good coverage. So is Revlon's Colorstay foundation.
Powder foundation might be a better fit, but sometimes you don't get as much coverage. I can't think of a drugstore powder foundation that has good coverage, although they may exist. If you pay a little more, Bare Minerals is good, as well as Laura Mercier mineral powder. Estee Lauder has a Double Wear powder, but I haven't tried it.
You can also try using a primer before you put your foundation on to help it last longer. A popular high end on is Smashbox Photo Finish primer. You can also use Monistat chafing gel. Sounds weird, but it's cheap and works the same :)
Another option is 'setting' your liquid foundation and/or sunscreen with powder. If you already have the coverage you want with a liquid foundation, something cheap and shear like Rimmel's Stay Matte powder would work great.
I'd be careful putting lip balm on your eyelids. Your skin is extremely thin there, and it may cause irritation to your eyes. If you want eyelid primer, there are some made specifically for that. Urban Decay's Primer Potion is a popular one. Elf even makes one for $1, but I'm not sure if it's any good. Personally I just use my face primer on my eyelids as well, and it works good enough for me. But hey, if chapstick works, I won't say anything ;)