Pool vacuum suggestions

I have a 14' intex pool that's 42" deep and I'm looking for a pool vacuum recommendation. I scoop out most of the debris but I'm looking for a vacuum that can handle the real fine stuff that's too small to scoop. When I scoop along the bottom I'll see a small cloud of get kicked up.

Does anyone have a recommendation of a vacuum that has a filter fine enough to handle that or that has an option to vacuum to waste so I can just pump it out?

Budget is a concern as I don't want to buy a vacuum that ends up being more expensive than the pool itself.