Re: .22 Bolt gun
A first 22 is just that, number one of several.
Like all things related to entry level firearms, I strongly urge easy steps and starting with basics
The Savage MKII F is an excellent starter 22.
My own early MKII F actually corresponds closer these days to the Stevens 300 (List price under $200), and I'd be very happy to recommend the 300 as a starter rifle, especially if cost is important. In my own case, cost is important regardless of my budget; I believe in paying for what I need, period.
That first rifle will become long appreciated for its basic simplicity and trustworthy performance. That's why I favor a full sized rifle, and the most basic Savage or Stevens introductory modles as starters. They work well, and they keep doing so.
I bought mine used 14 years ago. It's still my go-to 22. It has also taught marksmanshp to a lot of young people as the most quickly chosen in our youth marksmanship programs ('Black Beauty').
There's absolutely nothing special about the rifle or its performance. It just keeps on performing and the kids have always just naturally gravitated toward this one. We've all put a lot of bricks of ammo through it, but it never balks and it seldom even seems to need cleaning.
When heavier barrels, better sights, and slicker triggers become an issue, the Savage line has them too. But a longtime shooter always cherishes the simplicity and go-back-to reliability of their first 22. Choose that one wisely. I'd suggest choosing the Savage MKII F or the Stevens 300 myself. I did.
Greg