What size Aluminum 3 wire should I use to run 200 feet underground at 100 Amps
It can only be 3 if this is the service drop - if it's a sub-panel it needs to be 4-wire.

3/0 (000) should do it. There are MANY voltage drop calculators on the web, as well as tables/charts. I happen to like the one linked, but they are mostly similar and should all give similar results. Shoot for 3% or less drop at rated (or calculated) load.
 I added 10 feet to account for getting the wire in and out of the ground, rather than just the horizontal distance - wire length, not "as a bird flies" is the number that matters for length.

I prefer to allow for the full load (100 amps) rather than attempting to finesse 30A 240V dryer + 120 volt loads unknown; I've lived with an undersized feed and I'm not fond of self-induced brown-outs.