You definitely want to get a .22 for your first rifle. The Savage MKII is a good budget choice, but if you are going to be doing target shooting, you'll want something a little more accurate. You didn't specify what kind of shooting you will be doing: prone? benchrest? position shooting?
If you are doing position shooting, you will want a rifle with a proper stock for position shooting, with a rail for a hand-stop, etc.
The Kimber 82G is a great value in a single-shot target rifle if you can find one in OZ. The CMP program in the US had a bunch they just got rid of (called 'rusty' but it was really just preservative). Also good is the Winchester 52C and the Remington 40X, but both might be out of your budget. But if you have the funds, the ultimate in accuracy is generally considered the Anschutz 54-series actions.
You will also want to consider if you are shooting open sights, you'll want some different inserts to work with. If you are going to go with a scope, make sure you get one that has adjustable parallax down to 50 yards/meters or less.
Most shops generally will NOT let you shoot their guns, particularly rifles, but maybe you'll find an exception. Really what you want to check for is that the stock fits your body and the trigger feels good (hopefully they will let you dry-fire it with a snap-cap/dry-wall anchor). The most important things are the fit of the stock to your body, and the feel of the trigger. Those are harder to change than sights/scopes.
If you can tell us more about what kind of shooting you will be doing, we can help more!
If you think the 22 is too small....well...50 meters is WAY TOO SHORT for .223. Especially indoors. When I think of .223, I think of 100 yards as a starting point and 200 yards for a challenge. There are .223 shooters making shots at 600 yards accurately and consistently.
Again, are you doing position shooting, hunting, plinking, prone shooting, benchrest? That all matters to what gun will work best for you.