There are more options out there than you think! I know of one decent option I was looking at for $12K, and a Taylorcraft recently sold for $8K.
I agree there are a few options out there. Although a lot of people say they want a plane in that price range until they see what a lot of planes in that price range look like.
It is all boils down to how much work will it need or how long will it be before you need fabric or an engine. The ones I pointed out are more consistently in that price range and there are some reasonable flying examples. I have seen a few Piper Colts in the price range the OP is looking at as well. I have seen a few Stinson 108s for not a lot more than that although they needed work.
We bought our '57 172 for 13K. The owner had bought it and put a good bit of money in it (close to 5k for a windshield cylinder and several other things) then found he couldn't get a medical. Admittedly we took some risk in that it hadn't been flown a lot in recent years. When we bought it she was in annual and we have put just shy of 65 hours on her since September. There have been a few things we needed to do but so far nothing major yet. My co-owner and I are also in a bit of a different position than some we both volunteer at a warplane museum doing mechanical work, he is a mechanic by trade and working on his A&P, and we also have a friend who is an A&P/IA who will inspect and sign off on our work so this significantly keeps the cost down for the small stuff.
Prior to buying this I was looking at a decent 11CC Chief that was airworthy for $14,500. Unfortunately the guy doing the pre-buy talked me out of it. I say unfortunately because I found out after the fact the mechanic had a bit of thing with the owner and I think he was trying to find reasons for me not to buy it most being paperwork issues that could have been rectified pretty easily. Guess it just wasn't meant to be.
I have seen a few other Chiefs locally in the 12-15K range but they had rough paint and fabric and close to run out engines.
The nice thing about some of these bargain airplanes is if you are willing to do the work sometimes their parts are worth close to or even more than the whole. So if something major breaks you can still get some money out.
I know there are deals out there you really have to be looking and again both of these deals were local which is where I think the best deals can be had. Some of it is finding the right person at the right time.
