Yep, Wyoming antelope should be where everyone starts with a western hunt, not elk. Antelope are more visible and much easier to hunt on public land. They get you used to reading maps and understanding landownership and trespass rules, and won't physically wear you out the way elk hunting will.
Draws are not a mess, nor are they rocket science to figure out. But, to someone not used to them, they can seem a little like a foreign language. People will complain about them, but mostly because they want to hunt the best areas more frequently, or ever. That's not possible in places with public land and a finite resource.
Get yourself an atlas that shows the public land, and you'll be able to make a much more educated guesses about where to go specifically. It's really not very hard.
Also, not all of Wyoming's deer seasons overlap the antelope seasons. They do in many places, but not all. Spend some time on their site, so you can understand draw odds, units (which are different for every species in Wyoming), Walk-In Hunting Areas, Hunter Management Areas, the drawing process, which tags go to leftovers and things like that.