For entry level are you sure you want to go that high on a .22? I love shooting my 22s, but you will want to move up after a bit. It sounds like you have an interest in accuracy, that my man is an affliction without cure. You will want to stretch your range out and will probably become bored with the limitations of the 22.
There are a lot of 22s (new and used) for under 200 that you will enjoy for a lifetime. The 10/22 recommendation is a good one. For bolt action all the major manufacturers have viable options.
Good luck with whatever you get.