Play sand and pool filter sand are both silica based sands. Play sand is a finer, light sand. Pool filter sand is a heavier more uniform grade. If you do end up using play sand, clean it heavily. That stuff clouds BADLY at first. Pool filter sand isn't as bad in that regard.
Finer sand can look better but is lighter, so in a high flow setup (are worse, one with diggers and sandsifters) it gets kicked up very easily. I wouldn't use it. Pool filter sand is just about perfect in that regards because even if it gets kicked up it sinks very easily.
I've never noticed much of a diatom problem. I do get a build up over the course of the week of brown algae (assuming it to be diatoms) but it is no worse then the green algae that would build up over the course of the week before. Both require(d) glass scraping. The green looked nicer though.
If you want less problems though then go with aragonite. As I said earlier, it isn't a simple cheaper alternative. There are trade-offs that may or may not be worth it, depending on the individual. If you want worry-free then aragonite is the way to go. The main reason I used pool filter sand is because I knew what to expect and was willing to accept that (and it was a $100+ difference).