That's not quite right. European brands of rifles tend to have tighter bores than their North American made counterparts, with CZ's being among the tightest. Whether the outer profile is a straight heavy barrel or sleek sporter, the internal bore of a CZ is the same, and that is tight. That said, these tight bore barrels can shoot any ammo that will chamber (With the exception of certain sub-sonic, low-power specialty rounds). What you may have heard probably refers to having a tight chamber. A rifle like an Anschütz has a match chamber where the bullet gets engraved into the rifling when you close the bolt, and this is considered a good thing for accuracy. However, if you try to load a CCI stinger into this chamber, the longer case of this round will get jammed into the rifling, and it could even possibly push the bullet down into the casing plus crimp it as it jams into the rifling. Not good things, so avoid using stingers in a match chamber. CCI SV ammo also has a noticeably longer driving band on the bullet compared to brands like SK, Lapua, Eley, RWS, etc... and can be more difficult to chamber and extract a live round in a match chamber, but shouldn't cause any real issues. CZ has a sort of hybrid chamber I would liken to a Bentz chamber that is often used on semi-auto target rifles. It doesn't engrave the bullet into the rifling like a true match chamber, but it is close. Stingers might be iffy, but depending on who you talk to, some run them just fine in their CZ's while others wont touch them.
With your budget I'd seriously look at a used Anschütz bolt action rifle, you can always upgrade your scope later when your budget is restored, but this will be a rifle that will keep you happy for a good long time. You'll probably find yourself wanting to upgrade from a Savage rifle in a couple years, I know I did. Accurate rifle, but cheap feel/build, didn't satisfy me. The smoothness of the bolt and high quality out-of-the-box triggers of an Anschütz are just a pleasure to operate. CZ's can also be tweaked up fairly well. When you feel like plinking, a CZ can handle Thunderbolts and Golden Bullets no problem, so there's your cheap ammo for your plinkin' fix. When you want to punch tiny holes in paper, load it up with some nice ammo like Lapua and it should shoot very well too. For ease of shooting off a bench, a "Varmint" style stock is better than a sporter style, and shouldn't be too bad to carry around for the odd hunting trip.
