Whatever you choose, DO NOT use ballistic tips on antelope (I wouldn't use them on anything). We're talking softball-sized exit wounds. I think the 165 grn is a good versatile bullet out of the 06, but I would chose something more tame than an exploding missile.
150 would be more than enough for antelope. I would think 125 would be sufficient but I have never shot them. I have shot several antelope with a 115gr nosler partition in my 25-06. For the 30-06 150gr hornady interbonds would be a good choice, as would 150 gr nosler accubonds. just my opinions.
I use 168 Bergers without complaint. BC helps in high plains wind. I have shot bear and mule deer, DRT.
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The problem with the 125/130 gr bullets in .30 cal is that the BC is pretty bad. I tried them many years ago trying to work up a light ground squirrel load. After 150 /200 yds, the performance really drops off. Use 150s as my standard 30-06 deer load. Should work well on goats too.
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I would stay away from the NBT unless you want a complete mess with a bad shot.
Due to windy conditions last year, I used a 180-grain Barnes TSX out of my Sako .300, and there was minimal meat damage when shooting them behind the shoulder. Just about any bullet weight is going to do more extensive damage if you hit bone whether it's a cheap 100-grain soft point or a souped up, premium bullet. As has been stated, I'd stay away from the BT's due to the expansion / exit hole issue. Antelope are thin skinned and go down easy - no reason for a soft-ball-sized exit wound.