My first trip for antelope was near Laramie, but I hired an Outfitter. He picked me up at motel, and we drove out to a huge ranch. It was just us out there. I loved seeing antelope seemingly everywhere. I used a .280 Ackley Improved then, and missed several during the day out around 350, that cross wind was brutal! I can't judge the wind on those "short grass" prairies! another problem I had was that dang wind was blowing me and my lwt Mountain rifle around so bad! A heavier rifle works better, though varmint weight isn't necessary, but works swell btw, ha. I ended up shooting my buck as he came running by a snow fence I had sneaked up to and had wrapped myself up in ( to hold "me" still) I missed him at 100 or so (they are fast) and I hit him as he quartered away from me around 200, then again at 250 (not needed)
Later on I shot several antelope does here in Utah (draw hunts) I used that .280 Ackley again on two of them, but stalked closer, one at 75yds, another about 80. I then used a 6.5/284 wildcat (about like a .270 or 25.06 really) and a 6mm/284 (again, just like a 25.06) I even used a 300 winmag for one out to 350, almost cut her in two!) However, a Nosler 125 ballistic tip in your .308 will shoot as flat as you need! Its a good bullet on antelope/mule deer too. You want a good scope, of course and good binocs, plus either a set of bipods or, my preference, shooting sticks. You can find places to sit down and shoot and sometimes, prone. Its just hard to judge that dang wind! Good luck to you and have a ball!