Took this guy two years ago with a 30-06. I shoot a 165 grain accubond. I'm not the biggest guy in the world, 5' 8". I'm not saying it's the best, but it worked for me.
I've been happy with the 125gr reduced loads from Hornady for antelope using my 06. They're tipped with the SST and perform well. The last 4 lopes I shot didn't mind at all! All were under 400 yards.
Nathan’s stuff over at TBR is probably the best info you could hope to find. He’s done years and years of research for every load imaginable on game of various sizes and weights. He’s written a few books on the subject but what’s on his website should be informative enough.
Read the “Factory Ammunition” section and read about the different loads and what game weights are acceptable for those loads and at what distances.
Some of the info is a bit dated but you’ll find most of the top factory loads there since they’ve been around a while. Accubond, Partitions, A-frames, Sciroccos, Gamekings, Barnes TSX, etc.
Whatever load you know how to shoot at distance already will work, as noted antelope aren't hard to kill IF you can hit them. So I wouldn't waste time working up a new bullet versus learning whatever you already hunt with well. Wind can be your biggest enemy out there for antelope. If you're starting from scratch and only planning to hunt antelope you could go with some of the lighter 30cal bullets but I favor more universally useful loads myself so I'd probably shoot a 165ish bullet still.
I prefer monos and have hunted 7mm calibers lately so the 145gr barnes LRX from either a 7-08 or 280AI is what I've used on around 10antelope in the last few years. Buddies have successfully shot them with 165s from 30-06 and 300wsm as well.
I've shot a 30-06 for a long time and the only bullet weight I have ever loaded for it is the 165 gr. I feel that bullet works well on everything from coyotes to elk and moose. I've taken many antelope with my 30-06 and it performs just as one would expect.
For bullets all I have ever loaded are 165 gr. Nosler Accubonds and Partitions. Both work exceptionally well. Find the one that shoots the best in your rifle and load it up and go hunting. IMR4350 and H4350 are two very good powders to use in the 30-06.
I've used the 150gr SST with success over the years, having said that a 243 shooting 100grs has worked very well also. As mentioned before they are not difficult to kill provided proper shot placement.