To make normal nail polish last longer: Wipe down your nails with nail polish remover. Even if you don't have nail polish on it removes oil to stop it from coming off. If your nail polish ever comes off in big sections that's because there was oil on your nails. Then use a basecoat. They're clear and thin and in addition to helping your polish last longer it'll stop the color from bleeding onto the nails. This comes in pretty much every brand, so you can find one at your local drugstore. Then apply your color. Any kind works, but you could go for the long lasting if you want. Then apply a clear topcoat. Typically the slower it dries the longer it lasts, so if that's what's important to you take the extra time for a hard-ware one. Then use some cuticle oil on your nails when it's all dry. Sounds weird but it really makes it last longer. This will last you a good period of time, depending on how rough you are on your hands. You can also do things like wear gloves when doing dishes to prolong it even more.

Gel nail manicures are really awesome because they harden the nail and help it grow, so its very hard to chip/peel the polish off. But gel nail manicures can get expensive, so if you want to stay cheap the only other thing I could recommend is using multiple layers of a topcoat over the colored nail polish.