Thanks for your service and good luck on your endeavors when you get out. 

As for the .300 Weatherby and what rounds and range here we go.  I would sight it in for point blank at 200 yards, that will give you shots out to 400 yards without trying to dope the scope.  Now for the rounds, I am shooting a .340 Weatherby and since there are no other rounds besides Weatherby rounds that is what I shot when I shot factory out of it.  I found out that Weatherby and Barnes bullets make a very good marriage and that is what I shoot out of my .340 but then I reload.  Weatherby standard factory round used Horanady bullets for a long time, you can now get them with Barnes, Nosler, and Hornady from the Weatherby factory.  I am not that familiar with the rounds that Federal, Remington, and Winchester manufacture for the .300.  I would stay with a 168 grain bullet up to the 180 for just about anything here in North America. 

If you reload and you really need to if you don't you will find that you can make a tack driver out of that rifle with a little bit of effort.  Weatherby rifles are very accurate and if you do your part it may just surprise you.

First - welcome to the site. I'm not sure that I understand your question: "what range should I use?"

A .300 Wby has a practically unlimited (from a hunting perspective) range and can easily kill almost all N American big game at 500yds. Most hunting situations involve shots within 200yds; and if your talking whitetail deer (just playing the odds since its overwhelmingly the most popular big game animal in N America) most of those shots are less than 100yds.

If I were shooting any 30 cal magnum, I'd use a strong 200 gr bullet. You mentioned that you w3ant to be able to shoot out to 300yds. Best way to sight in? in my opinion it's to zero the scope for mpbr, max point blank range. Consider the size of a target yiou want to hit, the side of the animal is a target. That's a pretty big target though. Most people that sight in for MPBR use an 8" target. What that means is, if your zero'd for max point blank range at a 8" target, your bullet will never riwse over the line of sight and will be 4" below line of sight at MPBR. That is the range you can hold dead on the target and with a good hoild, in theory, hit the target from 4" hiugh to 4" low all the way out there. You decide which bullet you want to use and let me know the advertised muzzle velocity and I can crunch number's thru my cronograph and get you awful close. When I do that it also shows me where the bullet hit's all the way out and gives me the range where the bullet will cross down below the sine of sight. 

Think of it as you have a pipe running from the muzzle of your rifle all the way out to who care's where. The pipe is 8" in diameter. You fire the round and untill the bullet reache's MPBR, it will never rise over 4" and only falls below it at the MPBR. What it does is let you decide what kind of trajectory you'll have. The bigger the target the longer the MPBR, the smaller, the shorter. 

According to Hornady you could drive their 190 gr bullet to about 3100 fps. That would be an awsome load but I'd have to run it to tell you just how to sight in. Probably in the neighbor hood of 2 1/2" high at 100 yds and I suspect that will put you on the target at 300 yds but 4" low, no problem if you do your part.

Let me know if you want to have the number's for the loads. I can give you any bullet you want if you can give me an advertised velocity. If it's a Barne's TSX ntype, I have no data on the ballistic coefficent and that need's to be reaqsonably close to right.

I might add that the beauty of a cartridge like that is that it deliver's extrodinary power at normal range's.

Neglected the issue of the scope. I would trust a Bushnell depending on which it is. The problem is that a lot of recoil can ruin a scope. Most scope manufacturer's make a scope that would handle the reciol. Rule of thumb would be to used an upper mid range price scope to high end. I do have a Bushnell on my 25-06. It's very old Banner 3-9x. I tried a 4-12, I think that's what it was, Bushnell. Great price but the rifle, 6.5x06, destroyed it pretty quick. Took it back and got a Nikon and have been happy with it other than that crummy BDC reticule. Most company's that offer life time warrentees generally put it on a scope, hopefully, that is not going to fall apart under recoil.