OP, you don't say whether or not you're looking for a single shot bolt action or a reapeater with either a box or tube magazine.
If you're looking for a sleeper, as far as accuracy goes, there are a few banner advertisers that are selling surplus TOZ8 rifles at this time, for around $200.
These rifles are usually very accurate and come with excellent, easy to acquire iron, tangental type sights
I had one of these for about thirty years and recently gave it to the daughter of a friend, she just turned ten last summer.
We took her shooting and let her shoot it off the bench first, then offhand out to 30 yards.
She has great eyes and great hand to eye co ordination, that go along with good upper body strength.
It's a full size rifle, built for adults.
She loved it. She made the comment that "it's to bad it isn't RED" She would quite easily have taken any Grouse she came into contact with up to 40+ yards.
Neither of them knew I was going to gift the rifle to they young lady and after the shooting session I took the stock off, sanded it down and painted it with RED boxliner paint, which gave it a nice pebbled appearance.
When I gave her the rifle, I told her that it was HER RIFLE, DO NOT LEND IT TO ANYONE, especially your DAD.
She took me seriously and when he asked her if he could take it hunting last weekend, like most women, she closed that door immediately. He mom laughed and that made it worse.
Still, they're a bit on the crude side but great shooters and with a bit of work, their triggers can be amazing.