I'm in the same boat. Started studying 6 months ago. You have to decide if you want a regular tag or a special tag. Check the draw odds for antelope units for each tag type. Special will get you more unit options. Buy the Onyx chip for Wyoming. You can use that on your home computer to look at the private vs public land in each unit. Decide if you want to pay a trespass fee on private land. You can hunt antelope every year in units with left over tags if you have deep pockets and can pay a big trespass fee. Most of the units in the N. E. portion of the state are mostly private land and have lots of left over tags. Contact the Wyoming Game Dept. for the landowner list that allow hunting. The list is out of date but it is a place to start. You can contact the game warden for the area you are interested in and see if he has any leads you could follow up on.
You need to do some home work on your own. Most of the members here will give good advice but they aren't going to hand you a hunt on a silver platter. They all started where we're at and have put in countless hours of research to learn the units and find a place to hunt. They expect us to put in some sweat equity just like they did. When you learn enough to start asking specific questions about specific areas, they know you've done your part and they will be more than willing to share their information.........probably by PM...........
I've put in hundreds of hours looking now. I've Googled units and read everything I could find, I monitor 4 hunting forums, I've studied maps, the Wyo. Onyx chip, Google Earth, Mike Eastman's Antelope Book, I've got pages and pages of notes on specific units I'm looking at. I've studied the Wyoming Game Dept. web site.............and I've got some good tips from members on the hunting forums.
I'm kinda protective of what I've learned because it has come the hard way. I suspect you will feel the same way in a few months if you're serious about a DIY antelope hunt.
Or.........you could hire an outfitter...........
I don't know much yet but, I'll do my best to help you get started. Hope you enjoy learning the process as much as I do.