Along with your criteria of low maintenance, high privacy and very inexpensive you may also want to consider using plants that are practical around a swimming pool, this means plants that are relatively clean in regards to shedding or have large leaves that are easy to pick up and won't clog an intake filter like lots of small falling flowers and leaves do.

Several palms are fairly clean in regards to shedding and can give you some privacy. As far as the expense goes, I suppose that is a relative term.
Some varieties to research would be Trachycarpus fortunei, Chamaerops humilis and Syagrus queen palm.

You could do a dense planting of cannas between the trunks and might even have room for some succulents.

If palms are not your thing then you might consider some large espalier type trees such as Magnolia little Gem or possibly some narrow growing hedge plants such as pittosporums or podocarpus

I think it would be a good idea to visit your local nursery and see what they have to recommend for your particular neighborhood/ climate zone.

It won't take much to block the view of the pool from those houses. How about an arbor to the rear, with some lattice and vines?