I use Collection 2000 Kohl, cheap as hell but its great, any Kohl works though, but its pretty thick. I wear quite heavy eyeliner. For lighter applied eyeliner, Avon's Glimmerstick Diamond gear is great, its that kinda clay stuff, and its glittery and stays well.
Use concealer on your eyelids first to give it something to stick to, and then when you've put it on spray your face with hairspray. Doesn't matter if you use the cheapest brand then, it won't go anywhere!
For bottom eyeliner, you can't beat Boujour black eye pencil. I like to put on the inside rim of my eye (really dramatic look) and I find this one the best. It's quite smudgy but actually stays in place well and doesn't end up where it shouldn't be even on a night out!
Stila's are good. Also though, maybe if you use some primer/concealer, or something as a base you could prevent that. Most primers are invisible, so you'd only see the eyeliner. I don't know if you maybe have oily lids, but that could help some.