The Savage is an ok place to start, but I would buy a used one. Then get in touch with Sharp Shooters Supply and get either a 6PPC or 30BR barrel for it. I would also get one of the forend adapters from Sinclair and put it on the stock so that the forend is stabilized on the factory stock. Then, get the best scope you can afford, a set of flags, and practice.
Thereis nothing wrong with the .308. I have 2 and they are very accurate. No reason to burn that much powder and readjusting the whole rest everytime because of the recoil.
I have one in 30BR and it shoots better than I can at the moment. The 6PPC is the standard, and any tools you accumulate now will help if you decide to get a full custom rifle.
I spent alot of money trying to make a factory barrel perform, and it did shoot well on occasion. It is better to get a Match barrel and start there. With a rifle in one of these 2 cartridges you can learn much faster because the barrels and the bullets suitable for them are accurate enough for you to learn meaningful lessons on shooting in the wind.
Factory barrels will have you chasing your tail wondering why a shot went out of the group for no apparent reason and you will have to get them in tune everytime you shoot, which is aggrivating for someone new.
Better yet is to scan the classified's and see if there are any good deals on a 6PPC or 30BR and start there. Believe it or not, you will probably spend the same amount when its all done. Trying to learn to shoot with a factory barrel is a waste of time IMHO. Good Luck, and dont forget the flags!