Jay, I am actually looking for the exact same thing now and I have been researching it for far too long. Being out of college for only a few years and having just recently gotten married, money isn't exactly easy to come by right now. As such I have been looking for one gun that will do just about everything for a few years until I can afford to expand my collection for more specific purposes.
As far as caliber, most people are going to say that for an all around big game gun you will want something with more horsepower than a 270 or 30-06. I am not one of those people. I have pretty much settled on the 30-06 because as long as you hit your target in the right spot, it is more than capable of taking down all of the big game the west has to offer and it will do it with considerably less recoil than any of the massive magnums out there. The milder recoil is important to me because I also plan to spend a lot of time at the range working up good handholds and just plain having fun shooting.
For a specific rifle I'm pretty sure that I will be going with a Remington 700 CDL SF. I have always been partial to the smooth model 700 action and with the nice walnut stock and stainless fluted barrel, its hard to find a much better looking rifle in my opinion. I have looked into many other rifles both more and less expensive as well. Kimber makes some really nice stuff for just a little more money. I put some serious consideration into their model 84L but decided it just wasn't worth the difference in money for me. On the other side of the scale is the Savage Weather Worrier series. They are a really nice, accurate and affordable rifle but I personally decided I wanted something with just a little more class.
I could go on and on about this but hopefully this will get you started.