I live right in the middle of antelope country and pretty much finding antelope is easy, the difficult part is getting close enough to get a decent shot. You will find that the first couple days of the season they tend to be a bit stupid but by day three they are skiddish and will bolt at any little sound.
We have used just about every combination of gun and bullet available to shoot them and probably the best is something on the heavy side. Heavier for caliber bullets tend to be constructed heavier and hold together thus damaging less meat. Antelope are very easy to put down but what you want is to do that without tearing one all up. My gun of choice is a .300 Win mag and as long as I can get a rib to rib shot I don't waste anything. My son uses a much smaller rifle but the results are the same. His gun of choice is a .260 Rem using 140 gr. SSTs.
Shot this one off the neighbors winter wheat last year -
