All the new guns are pretty good, but buy the best you can afford. Savage is accurate but stocks and magazines are not ideal. Ruger American makes a better stock and magazine set up and the ones I have shot are very accurate. The next step up and it is a big one is CZ. Everything about them is good. Nice blued metal, a couple styles of nice wood stocks. And superior accuracy across the board, widely proven in competition. A used Remington or Winchester are good, as are some older Mossbergs. But I would still go CZ unless you can afford an Anshutz, they are the best in everyway.
Some guys like the Russian Biathalon rifles but they have really gone up in price and for the money I'd rather have an Anshutz.
Someone said you can buy a Savage then put a different stock on it, but then you would have been better off buying a CZ to start with. Occasionally someone will report a Savage out shooting a CZ, but that is a very rare exception. Rimfire Central is a great treasure trove of info all things .22. Modified Ruger 10/22's are big over there. I have one that is great, but if you prefer bolts, go CZ. My CZ's outshoot my Ruger. But at a Turkey shoot a guy with a stock 10/22 almost tied me as I won the relay with a CZ 452 American.