Hard to beat a 22lr
Hard to beat a 22lr for a first gun if you were talking rim fire. If you were talking about the center fire 22's out there then they are of course more expensive to probably buy and operate.
I bought one of my sons a Remington 22 bolt action around 10 years ago for Christmas that was around $130.00 out the door including 4x scope. It does not have the smoothest action but feeds every time and is great fun to shoot.
As for hunting 22lr is only good for small game and varmits. If you want to hunt deer here in Texas a centerfire cartridge is required by regulation. 22Hornet is legal but .243 is a much better choice IMO.
I have no experience with either the Savage or Stevens so I cannot comment on them. I feel I have gotton more bang for the buck buying used guns and then spending more on optics.
Good luck with you first rifle.
“Government does few things well but it does them at great expense” Cal Thomas “When Government Can’t Be Trusted” 6/11/2013