Antelope season will start early in October, and deer late in October, so if you want to do both, you will have to wait until late Oct.
The best thing to do (assuming you don't have a place to hunt), is to apply and see which licenses you get. Then, in mid-summer, call up Fish Wildlife, and arks (FWP) in Miles City, and ask them to send you the "Block Management Book" for Region 7. That booklet will come out in early August.
It contains general county maps and a list of all private ranches where hunting is allowed. You will need to narrow down the area you want to hunt, and then call FWP back and ask them for maps of the hunting parcels you're interested in. (I think they limit you to 5 maps at any one time).
Then make your decision on where you want to go, call the landowner, and reserve a time.
If you want to go for the antelope opener, you have to do this ASAP. That first week of antelope season fills up FAST!!!!
The landowner gets paid for this from FWP out of the nonresident license fee - so once you buy a license you've already paid for this service.
Especially for antelope, I think this Block Management Program (BMP) is a great situation. The ranchers generally limit the number of hunters and will only allow you to drive on established roads - so you never have that horrible situation (like often happens on public land) where you are putting a stalk on a bunch of antelope, and here comes a bunch of guys roaring along in a pickup and they stop and start blasting at the herd you've just spent the past 2 hours trying to stalk!
There were A LOT of antelope in Region 7 this year. If the winter is mild, next year should also be great.