While I find a .308 to be overkill when it comes to deer, you just can't do better than a new Savage. They shoot great and won't break the bank. I've purchased three new ones in the last 6 months and they are all sub MOA.
I think Savage bolt actions are real sleepers. Their good performance is out of proportion for their price.
Have you ever tried a scout scope setup? They're supposed to be fast, but I've found them to be much slower than a conventional scope or iron sights, especially a peep sight. If you haven't tried one, you might want try one first.
The scout setup is not strictly a short range only proposition. Depending on the quality of the optics it can be a 600 yd capable package. Using a scout configuration is much like how shotguns should be shot ... both eyes open. If you have even the slightest problem with this then go with a conventional eye relief scope. Otherwise the scout configuration can be really effective in nearly all hunting scenarios. The big thing is that you have to practice and not off sand bags at the range, you need to practice in real world conditions. Of course this goes for all rifle shooting but a lot of guys don't get that detail.
As for the rifle itself, you won't be dissapointed with the Savage bolt gun or the .308 Winchester chambering.
I am a Browning and Remington rifle fan.....but with that said the Savage IS the most gun for the dollar spent. They seem to have a secret on accuracy that many others do not. Go with one of the short actions !!