If deciduous, you are looking for something with an open/airy canopy, very small flowers, no fruit and one that doesn't shed leaves beginning in July, slowly through October. And preferably drops it's leaves over short period. Take that tree, of which I have no examples, and plant it about 150' away as Newdude says. I would ideally never want any branches even over my decking.
Actually, many trees planted about 100-150' away won't be too much of a problem. Better if the pool isn't downstream of prevailing winds. But do avoid trees with small leaves that drop from midsummer on. You never notice it until you have pool. Small leaves float on the surface to the side. Then each wave in the pool pushes the leaves up higher on the tile where they stick until you remove them. My example of that is a 'Sunburst' Honeylocust. All the great attributes except tiny leaves that fall slowly starting in about July.
20 years passes like the blink of an eye.
But life isn't perfect (and we didn't need 2020's shenanigans to prove that to us thanks). I planted a scarlet oak and sawtooth oak before we had any dreams of a pool. Their trunks are 50-60' from the water. Oh well. But the (our) magic answer is an autocover. You can deal with many spring/fall tree issues with one. Only drawback, the $15K lighter your wallet will be for it.
Evergreens aren't trouble free either. I cut down most of a row of healthy Leyland Cypress because they were so tall enough and old enough (20 years old), that when a high thunderstorm wind (50+ MPH) would come through from the correct direction, the pool got 100% covered from the dead internal tree litter in 30 seconds.