Speaking as a guide for antelope hunters, I would have to agree with those who suggest the .270 or something smaller. 25-06 or 243 is even better. Please do not take this the wrong way, because I don't know you or your ability, but it has been my experience that most of the hunters I guide tend to bring way more gun than they need or are capable with.
I would suggest a hunting trip with a rifle that you are very comfortable with for your first time. Learn the intricacies of hunting out here while you are figuring out the things you will need to know in order to have a successful long-range hunt at some point in the future. I'm not saying any of this to be discouraging at all. It's just that there are alot of factors that people tend to overlook when planning a hunt out here.
Wind, elevation and distance are the three main factors that seem to catch people off guard.Even with technology helping them out, hunters will still have trouble at times. Heck, I live here and I will question the range finder, or I will misjudge the different wind currents.
Wind is a big problem for people not used to wide open country. I have literally seen seven different wind currents over a span of a 1000 yards. To see that, you have to be set up in the right spot, but it does give you a good perspective on the difficulties you can face when trying to make a good shot at extended ranges.
Elevation is an absolute butt kicker for some people. I try to cater my hunts to a person's abilities, but even then, 5000 feet to someone who came from 400ft can be pretty strenuous. Don't under estimate the need for being in good physical condition.
To someone who is used to having trees or other reference points around, distances out here can make you question your sanity. You will want to throw your range finder away and go buy a new one, because you will swear the one you have is broke. It isn't. Many times I have told hunters to hold dead on because the animal is only 100 yards away, but they will miss because they think I'm wrong and they end up holding for a 300 yard shot. What you estimate to be 500 yards will usually not be more than 250, but that is just one of those things you will have to see and learn about.
The place I guide antelope hunters on is not a big place, but it is fairly easy hunting and it is rare that any of my clients have ever had to take a shot over 300 yards. Most people have harvested their goats at 250 and less. The only people I have ever had take shots over 500yards were two Navy SEALs and they were shooting 300 WM's. They knew they didn't need that much gun, but they were looking for bragging rights for when the got back to Virginia.
What I am trying to say and have gotten longwinded about explaining is, you really don't need alot of gun to hunt and harvest antelope. Something that shoots flat and that you are comfortable with is all that is needed. There is plenty of government land for a Do-It-Yourself hunt, or there is ranch land available for those who want to pay for trespass rights. People bring all sorts of guns and calibers out here, so don't get too bothered by trying to pick the right one. Just about anything will work.
Good Luck
Tex