When I was quite a bit younger, my parents got me the Daisy 880 that I'd been begging for for years. I must've put 5000 BBs through that thing in the first few days! I still have it, but it's pretty worn out now. I keep it around for sentimental value. I originally had a Tasco 4X scope on it, and I was deadly accurate for a kid.
The only problem was my arms would get so worn out from pumping it 10 times for every shot[that's what made my first .22 rifle SO enjoyable!].
At a gun show a couple years ago, I bought one of those break-open Chinese pellet rifles on a whim. It was less than $30, and I can't leave a gun show without buying something.
I put a 4X32 Simmons scope on it and refinished the stock. Man, that thing is FUN! shooting it brings back memories of my Daisy 880. Except it's a lot more accurate, it has a higher muzzle velocity, and I only have to pump it once. It's pretty dang cool.
Sorry for rambling, I think the cheapo Chinese rifle is a good buy. See if you can find one.