There are plenty of single shot options out there.
I've owned a handful of the NEF Handi Rifles. I think I've had .243s, .22-250, .223s, .270, .30-06. All have been decent rifles and all were bought for under $200. Might be something to consider if you just want to try something before dropping a large bill on a nice single.
The only one I had problems with was a used and abused .223 that had some ejection issues, but I got it straightened out.
You can find them on the used pages for around $150 most of the time.
-Jake