If you put on a new barrel, the best option for most folks would be 7.62x51mm, in order to be able to use surplus military ammo. The 7.62 NATO is still in use around the world, so there's a decent chance that surplus will continue to drift in, or that East European manufacturers will produce moderately cheap ammo for the American market.
For the .308, I don't believe anything needs to be changed besides the barrel, though it's advised to buy a little plug to go into the magazine to prevent 30-06 rounds from accidentally be loaded in.
There are numerous discussions of rebarreling from previous months, which you can find by clicking the Search button. Also bear in mind that 7.62x51mm and .308 are almost but not quite interchangeable, so some folks may advertise rebarelling to ".308" instead of "7.62 NATO".
I'd buy one case of surplus 30-06 ammo and shoot it as-is with the original barrel first: you might get one with a perfectly good barrel. Make sure to check and see if the 30-06 ammo you buy (such as Korean) is corrosive. If it is, you can still shoot it with no problems, but make sure to clean it fully as soon as you get home from the range. Run a Search under "corrosive" for info on what products to clean with after using corrosive surplus ammo.
-MV