I too would stay away from the larger calibers if it is just going to be a plinking gun or for small game. .22 is great for that, for the price you can't beat the Savage line of rifles.
I hunt (large game) with a .30-08 rifle, but it kills my shoulder if I just want to go to the range and shoot, so if you plan on shooting a lot and can't take the recoil for a long period of time I would steer clear of the larger Calibers.
.223 would be a good choice for all around hungting on small to medium size game and for target shooting. Here in the US we can buy surplus ammo for dirt cheap, not the best for ammo for extreme accuracy, but it works for just messing around. Not sure if surplus ammo is available for purchase in your country though?
One think to remember is that the price of ammo just keeps going up and up. Brass and Copper prices going trough the roof so if you plan on shooting a lot a .22 might be your most cost effective option.
Have fun, and I would suggest taking a gun safety class if you have not had too much experience with guns and shooting.