Wyoming will be your best first choice. You can purchase a preference point between July 1-September 30, and this will increase your chances in next years drawing. The better units usually take 3-5 points unless you're lucky. With 1 point there are some units with a lot of tags, and public land that you could hunt next year. Although they can be a bit of a free for all, you can get some experience, and your first one on the wall to look at while you wait for a better opportunity. Get a map that shows public land, such as the Delorme, and match your game unit map against it. A good GPS will help you know where you are at if you select a unit that is checker boarded with private land.
Montana can have a lot of tags, not generally considered good for quality. This winter has reportedly drastically reduced Antelope numbers. Maybe someone on the ground can tell us more. Antelope can come back fast if the coyotes aren't too bad.
Nevada plan at least 3-5 years of points to be in the race, 5-10 years more likely. To late to begin building points this year. You need to be in by April usually.
Other states drawing odds for non resident are getting worse each year, and unless you can afford a land owner tag, or a commission auction tag, it's probably not worth it. Example I have 13 points in Oregon, and figure I have about 3-5 years before I draw, dependent on the unit.
Apologies to the ladies, but hunting Antelope is about as much fun as a man can have with his pants on-good luck.
Being from Washington also, getting out of state will be one of the best things you can do for your hunting career.