I started out in the 70's shooting antelope with about every caliber you can imagine. In those days, you went to Wyoming, bought two tags for our area, then bought 5 more doe tags. The whole darn bunch of us had tags for about 40+ antelope. We read all these articles on long range this and that, no one could hit a bull in the arss with a bass fiddle. I shot my antelope, found out that the only way I liked to eat them was in jerkey, so about 5 was all I could afford to have jerked...best jerky on the planet.
When you skin the breeches of a full grown antelope, there is not much left. So, you don't need a 375 H&H like one of our guys had, or 300 win mag like 3 others' had, nor 7 mags like I took for the first time. I went down to 30/06, then 270, then 25/06 and settled on the Sierra 90g BTHP at 3300 fps or a 6 Rem with a 95g Partition at 3150 fps. The 25/06 still blows them up quite a bit on 200 yd shots. The whole idea of "eating up to the hole" is a bunch of crap with many 270 loads because if you hit them in the shoulder, you will more than likely throw away the whole front half of the goat.
The 270 is a cannon on goats, but for most it will be just about right. I love the 110g bullets in the 270, they are all unreal accurate and at 3400 fps you can buck the wind for quite a ways. Accuracy with the 110's with 58g of Win 760 or 57-58g of R#17 is in the area of 3400 fps and H4350 is right in there also. Hornady 110g HP, Sierra 110g Pro hunter, and Barnes 110g Tipped triple shock simply shoot benchrest groups from a std Rem 700 sporter in a Wood stock that has been tweeked with tuned trigger, bedded, and freefloated barrel. Neck shots are easy with high powered scopes or watch their skull caps fly. The 110g Tipped triple shock will shoot a hole through a deer from any angle.
The last buck antelope that I killed was at 470 yards shot with a Rem 788 in 223 with a hand load of 26.5g of Win 748 with a 55g Winchester, lung shot, he flopped in his tracks. I did have a range finder with target knobs marked on my scope 6.5x20x scope. 22/250's with a 60g Sierra HP, max load of imr 4350 are preferable to larger calibers, but everyone has to find their own way. Picking up a goat from the processor can be a humbling experience, with nothing left of the animal but what fits in one plastic grocery bag...I don't eat horns.
You can shoot a lighter caliber, or go for the horns on a long 5 day hunt that just made me stupid on several occasions. My crowd along with the ranchers like to get some meat at the processor, then go back to the bar, eat a lousy steak, drink beer, and lie about how good look'en the ugly chicks are that come in the bar...now that is what we call fun!
First couple of days on a goat hunt, you can get close to them, after that, it helps to have a dune buggy with a quiet muffler.
The longest shot that I made on a goat was about 800 long steps with a 270 shooting a 140g Sierra BTSP with a max load of H4831. I misjudged the range to about 550 yards when it was actually 800 yards. I shot and saw the bullet hit way low, then the antelope dropped...I bet that happens a lot.