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I don't start with the rifle. I start with the bullet.
I want the highest ballistic coefficient bullet I can get. (You can kill an antelope with any bullet made in America today, but you have to get it to him with sufficient energy.)
Turns out that 7mm bullets like the 168-gr Berger VLD and 162-gr Hornady A-max have the best B.C.s
Next I turn to the cartridge behind the bullet. That big B.C. needs all the muzzle velocity you can give it. The biggest is the Remington Ultra Mag. There are others just as good - STW, Weatherby, the Lazzeroni big magnum, the Dakota magnum. But the 7mm Remington Magnum, although not the fastest, is so close and so much more available that I consider it the best all-around 7mm even if it's not the absolute fastest.
The 7mm-08 and 7x57 will kill antelope for sure, but not with the flatness of trajectory of the big 7mm magnums.
Next I pick the rifle - a good single shot or bolt action, with a long barrel, and perhaps a muzzle brake if you've chosen the Ultra Mag or its brethren. A single shot will allow you as much as 30" of barrel or more, whereas a bolt action of more than 26" is ungainly.
Don't forget the barrel needs adequate twist for these long bullets. As I recall, the Hornady A-max needs 1-in-9", and the VLD needs 1-in-10".
Rugers, Browings, and many custom or semi-custom single shots are wonderful. All the standard bolt actions - Ruger, Remington, Winchester, Weatherby, Dakota, Jarrett, MacMillan, Cooper, the list goes on and on. They'll all do the trick.
Last is the scope atop the rifle. As a bare minimum a 3x-9x Leupold set to 9x. Many serious antelope hunters use tactical scopes like Nightforce, and high powers like 20x or 22x.
If you go that route you'll want a ballistics program, a chronograph, and a shooting range that allows you to check you're 1/4 minute clicks out to at least 500 yards.
Do all that, and practice, and you'll be a world-class antelope hunter. Make sure you wait for them to stop and stand still. Don't shoot at running antelope. And learn to judge horns. With a little practice it'll all pay off.