The Savage is a great little rifle and one you will not mind beating up a bit. But. I have a CZ 455 American and love the thing. It’s a great looking rifle, extremely accurate and can be swapped from 22lr to 17 HMR with a barrel and mag swap, which is very easy. 2 calibers in one rifle is nice.
It depends on what you want to do with it, for plinking the 10/22 is one of the best rifles going right out of the box, if it’s small game and some bulls eye shooting go with the CZ. If you want a super quiet tack driver the Savage is the only way to go. You can’t really screw up this decision, you’ll get a great shooter no matter which way you go.
I would also buy a bolt gun, keep the 10/22 and maybe do those upgrades later on as you can afford them.
I have a Savage 93R17 GV and chose it over one of the CZ models because it was cheaper, and has a reputation for being a tack driver. I think the same would apply to the .22 LR models. Cost of .17 HMR ammo is on par with medium cost 9mm ammo, about $14 for a box of 50, but the cost and availability of .22 ammo today is ridiculous.
I have a 10/22 I bought for $149 used a few years ago and have had no problems with it. Every time I think about upgrading the trigger, I look at the cost and say no. It’s a fun gun as is. No experience with the Savage or CZ in .22. You can’t go wrong with either of them. Savage for function, CZ for function and finish.
I used to have both a savage MKII FVSR and a 10/22. when I got my .22 AR upper I actually sold the 10/22. The FVSR is an awesome little tack driver with an over sized bolt handle, threaded 16.5" barrel, and comes with scope base already installed.
I added a BSA sweet .22, a boyds rimfire hunter, a 550cord sling, and an extra flash hider i had laying around for S&Gs till my stamp comes back.