I'm not familiar with your particular gun or BSA parts availability but spring break barrel guns are pretty simple to strip, though GREAT care needs to be taken to ensure the mainspring tension is released safely, I do think it would be a shame to give up on it without having a look inside.
As for replacements theres a vast range of guns available, spring guns are the cheapest, easiest and most reliable, I have a Weihrauch HW80 (break barrel) and a HW97 (underlever) both of which Ive worked on extensively (polished internals, ports opened up, lazerglide piston, brass set back trigger blade etc....) and they are both nice guns, the 97 is the smoother of the two and a joy to use but the breech loading area is capable of removing your fingertips quite easily if things go wrong (the only downside of underlevers imo).
Webley have made plenty of nice basic spring guns, I had an older Vulcan break barrel before the HW's that worked fine, you should be able to pick up a nice 2nd hand break barrel spring gun for £75-100. If you only shoot targets I would suggest a .177 for its flatter trajectory and lower power requirement.
There are loads of other good makes, pick up an airgun magazine if you can (Im a bit out of touch and havent used my rifles for some time) I would avoid the cheap Chinese models.
Jason