Try and find an old Mossberg 152K! Apparently the old Mossberg barrels were "lead lapped" which is a process that fills in the micro-cracks in the metal producing a very smooth surface with very little variance or imperfections. It is also very labor intensive and, as a result, expensive. The process is only applied to the most expensive target rifles these days.
I got one from Ellwood Epps a couple of years ago that was nearly new for only $120.00!!!!! It is amazingly accurate and only weighs about 5 pounds! I had mine out to the indoor range last weekend to sight in an old Weaver K4 that looks very nice and period correct on it and was cutting 1 small ragged hole at 20 meters with the crappy federal bulk blue box ammo. I can't wait to see what she really likes to shoot! It is also a very short and handy little carbine with an 18" barrel and overall length of 38". The takedown of the bolt is the best I have ever seen. You can unscrew the rear of the receiver "cap" with a nickel and the bolt just slides out the back so you can clean it from the breach like a bolt gun! By far the best design of any semi .22 out there!
I highly recommend one!
Cheers,
Ian