I think AC is used, because wet clothes weigh a good bit, so you need a lot of power. Best bet would be to look through some appliance repair sites and see what's being used, and how it works. Haven't had to do repairs on the washer machine, had to do the dryer a couple of times. Both old machines. Takes some looking for the free information, but it's out there. Ususally the sites that sell parts have online repair guides.
Not sure what anyone can do in designing a machine from scratch. For speed, guessing you only would need a couple, plenty of AC motors in that area with 2 or more windings for selecting speeds. Haven't really taken much interest in it, but think there is just a slow speed for agitation, and kind of fast for spin-dry. Never messed with anything more than the basic wash cycles, don't wear anything delicate....