Your choice of the .308 is an excellent 1! My favorite deer cartridge, it's available virtually anywhere, as well as being an accurate round.
1 question - are you only looking at new rifles? There are some good deals in used rifles these days, and you can really expand your knowledge with a little research. All of the bolt actions that have been mentioned are excellent quality rifles. But there's more out there!
Me, I like rifles/guns that are a little 'different'. For instance, my favorite .308 is an old Winchester Model 88 lever action with a 4x Weatherby scope. It fits me the way a rifle needs to, and hits everything I shoot it at, as long as I do my part!
The Remington pumps are good rifles too, I have 2 in 30-06. The 7600 will shoot in 3/4" at 100 yards with any 165 gr. load. I just traded for an older Model 760 and haven't had a chance to shoot it yet.
What I'm getting at here, is a lot depends on how you're looking your 1st rifle. Is it going to be strictly a tool, or do you look at it as the start to a vast collection???
I know that when I was 13, I wanted a 'wall full' of rifles, as I loved to hunt, and wanted to go after game all over the world! I bought my 1st rifle at 15, an old, beat up 7mm Mauser with a foggy Weaver scope.... I spent $75 on it, which was a pretty good chunk of $$$ for me in 1976! The local gunsmith/gas station owner said the barrel was warped, but I could consistently take out crows up to 150+ yards, so I was tickled to death with it!
Until! the time the scope fogged up on me, with a beautiful 10 pointer picking his way down a trail about 75-80 yards off, and I couldn't shoot because I didn't want to wound him, and wasn't confident taking the shot. I've been kicking myself for that for over 30 years, and I can still see him today.
Buy a few different boxes of shells(a good bet are any 165-168 gr loads, as every .30 caliber rifle I've owned has shot that weight better than any others!) and shoot it! If it's a new one, follow the manufacter's recommendations for breaking in the barrel - it makes a difference! Shoot different bullet weights, styles and brands. You'll eventually find a couple of loads that are more accurate in your gun, and you'll be getting good with it!
1 reason that I like my old 88, is that I trust her completely. As soon as I've made a decision to shoot, the deer falls, as if she acts on her own! Hopefully your's will treat you as well!
I know this is a lot to think about, but it's your 1st deer rifle. What ever you pick, it sounds like you're going to do a fine job with it - hunt safe and kill clean!