Don't get a 10/22 if you want a bolt gun.
I think you're right on looking for a good quality bolt action. Th CZ and the Ruger 77/22 both fit as does the Kimber and some others.
In my local gunshop today I saw a nice Ruger 77/22 with laminated stock and Leopold Scope used for $550, and it looked like new.
While I like open sights, especially to learn with, and on a first gun, there are some great bargians out there in the used gun catagory.
Check the rimfire forums, and the .22 forums to get other points of view, and don't worry about pistols and revolvers yet. You can learn so much and get so good with a bolt action rifle that there isn't anything better to start with.
I still shoot mine all the time after 50 years, single shot, open sights, and I love it.