Where in NKY are you hunting? I'm over by the Bracken/Pendleton/ Robertson/Mason line. In fact, I'm looking at all of them right now from my front porch.
A Rem 700 in 308 is going to be perfect, but so would a Savage or Ruger or Winchester. Me? I like a 3-position safety like the Winchesters or Rugers. The next guy is going to say tang safety. If I had to tell you the best bargain of all of them, I'd go with the Savage with the AccuTrigger or the Ruger All-American or the Weatherby Vanguard. It's really all about taste more than fact. In Northern KY, you will never have an action freeze in the cold or a barrel rust from 5 days of rain. You will be home with your deer in the freezer before the Thanksgiving leftovers are all eaten and the first significant snow falls in Dayton. Your lungs will never tear at your chest from hunting at altitude. The Big One will probably walk out at 50 yards and not 500.
Find the rifle that fits the best. Remember you will be wearing heavier clothing, and there is a significant difference fit from a T-Shirt to a sweater and parka. Stainless? Honestly, rifle season has not been all that hard on my firearms. All are blued steel on wood. I keep a couple of them home when it rains. However a quick coating of car wax usually is all the prep I need. After the hunt, I'd recommend Ed's Red and Eezox.
If you would like good alternative to your plan, think about a used Rem 7600 in 30-06 or 308. It will get you into the field a lot cheaper. It is about as accurate as the 700, and the pump is a little faster cycling than the 700. I hunt with one in 35 Whelen, and it is a super deer killer. Stick a $40 BSA 3-9X scope on it from Sportsman's Guide and you're on your way. It's a good idea-- didn't say it was better.
Having hunted around here for 30 years, I can't think of a thing better than your choice. My #1 pick for opening day is a .308 Savage 99. However most of my rifles are 30-06 The majority of us at camp have 30-06. My rough guess is the majority of folks around my county hunt with 30-06, 308, 270 or 30/30. A few are using .243 On my farm I take the majority of deer fairly close from a treestand. However, more and more of our late season deer are being taken at 150 yards or so. Remember that a short-action 308 may actually have more felt recoil than a long action 30-06 due to the weight of the receiver. Outside of that, for where you are going to be using it, there is not appreciable difference. 150 grain or 165 grain Green Box Remmies should work just fine. There is going to be no need for premium ammo. I shoot 150 grain bulk Rem PSPCL or 165 Hornady Interlock in all my 308 and 30-06 loads-- between my sons, and myself that's 9 rifles.
In regards to scopes: I've never paid more than $100 for a scope. Most of my shooting opportunities are inside 100 yards. The demands on the scope just aren't that great around here. About the time legal hunting begins, you can see through your scope. About the time it ends, you can't. What more can a deer hunter ask for? I've gotten by with Bushnell Banner, Simmons, and a few nice BSA's. Having said that, a buddy of mine showed up with a nice Nikon scope a couple years ago, and I was mightily impressed with the difference. However, I understand the problem of budget. I'm still crawling out of 2.5 years of unemployment and 1.5 years of under employment j at DP&L. I'm just getting back on my feet. Don't feel you need to throw $700 at a scope. My biggest bucks have all been taken, looking through a $40 Simmons 3-9X purchased in 1985.
Be sure to check out my weblog (see the link in my signature) There are gobs of stories about hunting in Northern KY, picking the right rifle, etc.