Stubblejumper has a point. 'Most' rimfire scopes are 'low-magnification' and so OK for 'hunting' but if you want target shooting scopes, I'd go for the most mag you can find/afford. I personally prefer scopes with numbered 'bars' (MOA or MIL) so I can make 'quick holdovers' for changing distances/winds w/o having to move the zeroed reticle. I bought a Bushnell Engage (6-18x50 FFP)when I first got a $$$ scope for rimfire, but soon moved to one with numbers on the bars. Used name brand scope would fit your price range.
No most rimfire scopes are built with a shorter set parallex, and not as robust due to the lower recoil. Don't need to handle as much Gs as something with higher recoil.
Like spring rated Airguns, they destroy scopes due to their forward recoil, so there are scopes built to handle that.
The OP is looking for adjustable parallax, so there is no fixed parallax. There is zero disadvantage to using a scope not designated rimfire, if it has adjustable parallax.
I'm well aware, I'm just commenting on the whole rimfire just = low mag, when it's not true.
Hawke is a brand I'd consider. Sightron the other. I got a bunch of old Tasco AO. I'm probably gonna replace my 8-32x44 Tasco AO with a fixed Luepold 24x.
OP never really told us his purpose.
Purpose... main purpose is target shooting out to about 300 feet max with the option for hunting around half of that distance.
The OP is looking for adjustable parallax, so there is no fixed parallax. There is zero disadvantage to using a scope not designated rimfire, if it has adjustable parallax.
Look into the Hawke line of scopes. Airmax and vantage.