Of all the hunting Ive done with Goats, any "deer hunting" rifle will be adequate.
Don't over think it.
Antelope are awesome and fun to hunt and make excellent table fare.
Ive seen them shot with anything from 243, 308, several 30-06's, 6.5 Creed, 300 Win Mag. And seen them shot from 65-345 yds. And any rifle from cheap Savage Axis', Savage 110s, Rem 700s, Ruger m77s, Tikka T3X's.
The 300WM was shot with 150gr Winchester XP bullet and didnt spoil any meat compared to any of the other calibers. Theres zero differences shooting a 308 or 30-06 at 65 yds compared to a 300WM at 200-300 yds or vice versa other than the speed at which the projectile is traveling. Speed is what makes the bullet expand. And modern bullets are designed to work fine from 0-500+ yds.
I would recommend being comfortable shooting out to 400 yds.
Id also get comfortable shooting in windy conditions, becaues WY the wind can whip around quite brutally.
This past Oct, my dad had his 308 and had a very nice goat with about 15-20 does at 400 yds crossing in front of us at 300. We crawled up to a knob and were belly crawling to get in position in shin high grass. I was shocked that the does in the group busted us immediately as we just barely crested the knob. Wind was howling, cross wind shot. The buck didnt care at all. But the does got uneasy and started to herd off, getting as close as 300 yds. This was the last morning of our hunt and I was trying to coach my dad to pull the trigger. He could never get in position nor comfortable and they trotted off.
I was a bit ticked and kinda got on my dad for the missed opportunity because I REALLY wanted him to connect.
We left and went and grabbed lunch. Came back around 2pm and found the exact same herd, same buck, in the same place bedded on the downwind side of the hill. This time, my younger brother went with my dad and crept up behind them and set up in a little valley behind them and waited them out while I watched on from 600 yds away keeping an eye on the herd allowing them to creep along. They got 65 yds and the buck got up and fed down the slope across from my dad. At 65 yds my dad was ready and waiting as he crossed broadside and the rest is history.
My dad felt vindicated for not pulling the trigger at 300 yds and possibly making a bad hit in the wind or pulling the shot. I felt better and glad my brother was with my dad because I dont know if I would have had the patience to wait it out.
As for a scope, a 3-18x will work just fine. Lots of options for any budget.
My first goat was with a 3-9x40 Leupold VX1 and my 30-06, Rem 700. Worked beautifully.
Again, any deer rifle with modern bullets, 400 yds and pretty much any scope will work fine. Same with binos. My older brother had $150 Vortex Crossfires and my younger brother and I had Swarovski NL Pure's and my dad had Redfield Rebels. Rangefinders from Leupold, Vortex to Fury RF binos.
Again, dont need to over think it.
You'd probably be better off just practicing with whatever your comfortable with.