You'll find that with most better guns accuracy is more dependent on the skills of the shooter than the abilities of the gun. The difference between side lever, under-lever and break barrels in terms of accuracy is small enough that the average shooter won't be able to tell the difference. Any quality gun can be very accurate in the right hands. Many matches have been won by break barrel guns as well as fixed barrel. My old Walther 55 is a break barrel, and its every bit as accurate as my side lever fwb300s target rifle. Both are strictly paper punchers though, purpose built match rifles. I also have a .22 Webley Xocet break barrel carbine that can produce dime size groups at 30 yards and a side lever .22 Diana 54 that will do the same. If you are looking for an all around gun for both hunting and target shooting there are more than a few available- guns from Diana, Weihrauch, Webley, and more all fit the bill. All you need to do is decide how much you want to spend, and start looking.
There are a couple decent peep sights out there, mostly made by Williams. The 22 rimfire trap works quite well, I've used one for some time now with no problems.
