Glad to be of help. Others undoubtedly know more about all this than I do, but I'm happy to share what I have learned. I also find it reassuring to know you don't need to try to break in at the top of the benchrest world if you want to start slow. I have so much fun at this that I like to encourage others to try it.
A "heavy" barreled 10/22 will work also, but it is likely to be not quite so accurate as a target-barreled, Accutriggered Savage. I have a re-barreled 10/22 with a target hammer (that lightens the trigger pull a lot) that I shoot benchrest with. But you're right, it's hard to be deliberate and careful for each shot with a semi-auto.
It might be a good idea to start practicing at 25 yards, which will give you an idea of what kind of shooting is required. Then move to 50 yards, which is a whale of a lot more difficult. I can clean a target at 25--most people can--but I can just barely make 90% scores at 50.
This discipline really teaches you how to use a scope much more precisely than plinking or hunting does, but it has a good carry-over. No squirrel is safe after you learn to shoot benchrest!
By the way, you can also shoot .17 cal. in USBR matches and .22 mags, although it is hard to find a really accurate .22 mag. I have a Marlin 982 that does reasonably well at benchrest but it's a good day when I break 200 with it.
In addition to this forum, you should look at RimfireCentral.com - Rimfire Community!
. They run monthly internet benchrest contests with a lot of categories of guns, including both 25 and 50 yard matches. You shoot four targets and submit your best score. I find that a lot of fun, although it's hard competition, because it gives me a reason to concentrate instead of just practicing.
You can also trot out your centerfire guns. We shoot centerfire contests here at 100 yards with ten bulls. A good hunting gun in .223, .22-250, or .243 with a high-power scope can do OK, but you can really see the difference when someone brings out a custom-made benchrest rifle in 6mmBR or .37-40. Those guns (with really expensive glass) are really in another league. Most of our hunters like this kind of centerfire shooting if they are into antelope or varmint hunting, because the skills really transfer. Many of them have really nice Sakos, Rem. 700s, Tikkas, tuned ARs, etc. I bought a very old fashioned H&R varmint gun in .223 just to get to shoot in the centerfire matches. It has a shockingly good barrel on it and can do less than MOA at 100 yards, but it's no competition for the really accurate guns.
Anyway, good shooting to you--I tend to run on and on about this topic.