I had this same dilemma when I had to pick a lot to build out house on. Here is what I went with. The lot lines in our neighborhood almost exactly line up with true North, South, East, West. I went with the front of the house facing South, This put the backyard facing North. In Indiana (and Ohio) this means that the portion of the patio closest to the house will always have some shade because the Sun never goes directly overhead (based on latitude). In the summer more sun, winter less sun on the patio. My pool sits far enough away from the house that the house never blocks the Sun. However trees in the yard could depending on their location. In the Winter, my driveway (facing south) is normally ice free because the sun hits it all day and melts the snow/ice. The family behind me who's driveway is on the north side, ALWAYS has snow/ice in their driveway. North side and low Sun isn't enough to melt the ice. I know that's "off-topic" but worth noting. My 2nd choice would be afternoon Sun, so backyard facing West. We normally use the pool in the afternoon / evening and as much as I hate the sun in my eyes, I'd rather it be sunny than in the shade all afternoon/evening. If you like to sunbathe, that would be even more important unless you are a morning swimmer.
The only other thing that would have swayed my choice would be privacy. If I could guarantee future privacy, I would have taken what was available. lol
