Electrical – Is aluminum Underground Service Entrance cable safe for a 200 ampere service

If you're running it through conduit, just buy single strand. It's cheaper. e.g. this
And obviously you'd be buying this at a proper electrical supply house, not the bigbox since they probably will not have it, and bigbox is really overpriced anyway. With wires of these sizes, it is not required to buy white or green wire for ground, you can designate that with tape.

Besides, it'd be murder to pull a 4-wire cable through conduit. Four single wires will be tough enough! Might want to bring in a commercial electrician simply for the pull because he has the gear on the truck to do the job easily.

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.