Changing a caliber... .223 is a short action so your action will work for anything that is also a short action caliber, such as .243, .260, .308. The 3 I just mentioned all use the same bolt face, so that is no concern. If you start with a .223 and change it to one of those three you will have to change the bolt face, as the .223 is a smaller cartridge. Long action caliber, like .25-06, 270, .30-06, all work on a long action, and you will only have to change the barrel if you stay within those specific calibers.
Changing the barrel on a savage isn't too hard with a few specific tools. This is one of the best step-by steps I've seen.
Stock (assuming you put same thickness of barrel) and trigger do not have to be changed, although a lot of people like to put a better trigger on while they've got it apart.
Of course this is just a basic idea on what you have to do. There are specific things you need to do in order for the rifle to be safe to shoot afterwards (ie, headspacing with go-no go gauges which is covered in that article). Also there is a ton of information on here if you do a couple searches.