Congradulations
Your 06 should do fine especially with 150 or maybe 125's. While small, antelope can cover much ground in a short burst of speed, so enough gun is required. Friends have lost antelope that dodged over a hill into large flat basins. Tracking is usually difficult in the antelope country we hunt, but mostly one can see the animal fall. The worst problem is breaking legs, they can go for miles.
Aside from longer shots due to open country, the worst enemy you will encounter is probably the wind. For this reason, we like longer bullets and a bit heavier calibers. The difficulty encountered in an antelope hunt varies greatly with the terrain and amount of antelope. Some of the units here in Wy. are very open and the antelope seldom see people, so when they do, they are moving off. These antelope are difficult to get close to for a decent shot. I would highly recommed a bi pod if you can fit it to your rifle. On other units the antelope see folks every day working cattle, doing routine chores, feeding, etc. these antelope are much easier to approach and we have shot a number with revolvers. They are a great game animal, and deserve to be respected for their beauty and unique role as American game animal. While a light caliber like a .243 is often recommended for these game animals, it works well at times and at others is lacking in killing and knock down power. Especially,
as ranges lengthen. Most antelope I have seen taken are at less than 350 yards.
I have no experience with Nev. But in Wy. they are plentiful and one of my favorite game animals to hunt. They make excellent jerky.
Best of luck.