For the last 2 years we've gotten a snap set pool from WalMart. It's about 18 inches deep and about 8 foot wide. It's not inflatable, so there's nothing to pop. The water in the pool keeps the sides up. The bottom is made of vinyl, so it's really tough. And if it gets a hole in it, duct tape fixes it. We paid around $20.00 for ours. They get a LOT of use, so we wind up buying a new one each year. We just don't have a place to store it in the winter.
To keep the gunk out, you can get one of those floating things and put chlorine in it. A friend of mine has one and she actually uses pool chemicals in hers. She shocks it once a week to keep the gunk down. You can buy covers for them too.
We just use a net to fish out the leaves and stuff that fall into it and drain about once a week or so. We don't pay for water (have a well) so it's not a big deal.