If you are looking at doing things on the cheap, go to your local pawn/gun and pick up a used 110 (or 10) series rifle. I would stick to these actions as the aftermarket is build around them. Do some reading here to help identify what you are looking at. .308 is one of the most prolific rounds in the US, so finding one shouldn't be much of an issue. You can then start to build it up as you see fit, or when the addiction really takes hold. The .308 is just fine for deer hunting, and so are any of its daughter calibers (.243win, .260rem, 7mm-08, .338fed, .358win) but the lighter rounds (>7mm) are much more accurate at long ranges due to increased BC of the round.
You seem to not know exactly what you are looking for, so please give some more details on what and how far you will be shooting this rifle. Most importantly, what is your budget and how much of a tinkerer are you?