if you're wanting to target shoot, then there are 'target' type single shot and repeater Savage rifles..... want are you wanting to spend? target stocks, longer barrel, heavier, different port configurations and specific target chamberings like 6NormaBR,6.5x284Norma, 308Win(&Palma) in addition to 223Rem...
But starting off I think its advisable to start with a rimfire to learn the ropes, operation safety function, but if you want to jump right in to centrefire, why not.....
The 223Rem has very mild recoil, and you'll happily shoot it all day on or off the bench, while the mid recoil 30 cals, are manageable but if you want to avoid a flinch, you really need to master them with lots of rounds, regularly shot, a couple hundred at least.
If you go out to the range and fire off 10 or twenty rounds, once every few months......stick to the 223 initially.
Milsurp are a lot of fun, but again, lots of rounds to 'learn' the recoil and butt-plate
You'll find 303 at most/all dealers, there are a few more brands, even in cheaper 50rd packs
