7-08 is definitely a good round. If you do not reload, honestly, I would lean towards a 308. The 308 has some of the best "factory" type ammunition that a person can lay hands onto. I do not think there is another round out that has half the *GREAT* off the shelf choices. With the right ammo a 308 can either be a pussy cat, or a 500++ yard hunting hammer. As for match type shooting, a well set up 308 will do 1k easy enough.
Nikon makes good scopes for sure. Hope I don't catch hell...but in all honesty I would not go with a BDC. I would go with a Mil Dot scope, and learn to use the mil reticle. Once you figure out a mil reticle, it makes life a lot easier pretty much no matter what you are shooting at.
Nikon 4-16x42 Monarch Riflescope
I would go with this model right here. Having Parallax adjustment for longer range shooting can be fairly important. The 4x setting is decent for when you expect game to be up close and a fast shot is required, yet you still have 16x for longer range, like 1k.
Many years ago, I was a real Remmy fan. The last decade or so, Remmy has been pretty hit or miss on getting a good shooter out of the box. Hate to tell you that, but good shooting factory sticks can be real hit or miss in general.
I have had a few people say that the new Made in South Carolina Winchesters are shooting real well. They are made by FN, who also makes FN branded rifles using the same action. The triggers are pretty decent these days too.
Some folks say the new Savage rifles are real accurate, I have not really played with the Accu-Stock models however. I have heard some people cuss the accu-stock, and others proclaim it to be the 2nd coming. I do like their trigger.
What ever you decide on, if it ends up being a 308 for LR hunting, I would *NOT* get a tube longer than 20" unless you plan on really hammering out past 800 yards on a regular basis. Even then if you get lucky and get a Good Tube, 1k is still doable.
I will say this.... RELOADING WISE .... winchester brass, winchester LR primers, Berger 185gr Hunting VLD, and Alliant 2000MR powder...and you can hammer out pretty close to 700 yards with adequate retained energy and velocity.... brutal ...in 308