IMHO (given the budget of $250).....
If I wanted a semi auto. I'd go for the Ruger 10/22.
If I wanted a bolt action. I'd go for a Marlin XT 22 or find a used Marlin or Glenfield 25 (or 925).
If I wanted a lever action. I'd go for a Marlin 39a or 39M. But, these are out of the price range that you have set.
Anyway.....make sure that you can find magazines. Some older rifles are difficult to find magazines for, And, some magazines can be expensive.
Why.....Ruger 10/22? Because it's like the AR of 22LRs. Meaning that, accessories are available that could turn your Plain Jane Ruger 10/22, into something more suitable for whatever direction you want to take it.
Why.....the Marlin bolts? I happen to love Marlins. Magazines can usually be found for decent prices even at Sportsman Warehouse and Cabela's. The rifles are accurate enough and they have proven records for reliability.
Scope? You can spend a fortune on just a scope alone. But, if you're looking for a budget scope. My I suggest a Simmons 22 Mag. 3-9x 40mm. They can frequently be found on sale going for about $35-$40 (or a little north of that price).
BTW....I got a Norinco JW15 a long time ago at a gunshow. Anyway.....here is a teaser.
https://www.youtube.com/watch?v=GzZUUE5zJWU
They are not imported into the USA anymore. Finding extra magazines was difficult and expensive (CZ magazines can also be used). If you can find a good one at a gun show.....you might want to consider it. They can still be found at an "under the radar" price.
Tube magazines aren't my style. So, unless it's attached to a lever action rifle.......I'll pass.
Aloha, Mark