Really late jumping into this thread, but hopefully I can offer some advice. We've hunted them every year in WY since the early 90's, plus a bunch in NM and Nevada.
1) Drawing a tag outside of Wyoming and Montana takes time. Sometimes a lifetime. We apply in every state that offers antelope hunts and so far, WY has consistently been the easiest. You can literally hunt there every year.
2) The amount of money that you mention is more than enough to enjoy a really nice hunt. It won't get you a hunt in NM, or an outfitted hunt with folks like Pronghorn Guide Service (check out there facebook page if you want to see some dandies), but it absolutely will get you a nice guided hunt in Montana or Wyoming.
3) Which leads me to my next point- you don't need a guide to hunt antelope. Although guides can be helpful in judging antelope- and often they are also the best option to get a good NM ranch hunt- a DIY for pronghorn is fun, and couldn't be easier to put together. Our annual approach is to put in for a difficult unit in WY as our first choice (57, 60, 53, etc.; basically the south central units) and an easy draw unit in the eastern part of the state (usually around Douglas or Gilette) as our second. We usually don't draw our first choice (but have been blessed to draw a few great tags over the years, and build preference points in between), do draw our second, pay an access fee to the rancher and go hunt for a couple days. Fly in and out of Denver, stay in a Holiday Inn Express, eat lots of Mexican food, easy! All in, it's about $1,000 per person with flights, tags, etc, and a fun hunt with lots of animals to look over.
4) I'd also strongly recommend applying in Nevada. They make you buy a nonresident license to apply, but for minimal money after that you can put in for antelope, elk, sheep, mule deer, etc. Over the years, Dad and I have both pulled elk and antelope tags and the quality of the hunt is exceptional. Great trophy quality, tons of public land and really good outfitters.
Hope that this helps. If you have any specific questions, please feel free to ping me.