RE: Gettin my first deer rifle.
Good choice on the 7mm-08, though the .270 would have been just as good.
For your price target of $350, take a look at the Savage lineup. Wal-Mart usually has a few Savages that come with an inexpensive scope about that price range. The scope won' t be up to the Vari-X II standard, but you can always swap it out. Who knows, maybe it' ll be good enough to get you through a few seasons.
For a little bit more, take a look at the Tikka line. A few weeks ago my will-power failed me and I couldn' t pass up an opportunity on a Tikka Whitetail Hunter in 7mm-08 for $465. Sighting it in over the weekend I had a couple of " cloverleaf" groupings (from the benchrest of course, I' m not that good!). All that right out of the box, no trigger work, bedding, etc. I think its a good gun, better perhaps than Remington and/or Winchester, for several hundred less. Worth a look anyway.
One closing thought - if you find a rifle that you like, for the right price, but its a .270, take it anyway. The difference between those two is not all that great. Certainly not worth passing up a good deal for.