From my own research, a mid-arm is generally anything from 13" to under 17". Anything 17" or over is generally considered a long-arm. Your average sewing machine is a 7" throat; there are some machines that have 9" throats that bill themselves as "mid-arms", but really, they're only slightly better than a regular sewing machine. The first machine I bought for frame quilting was a Juki with a 9" throat, and I found it impossible to work with; I know there are plenty of people that are able to work with machines that size, but I didn't enjoy it!
If you're looking for something affordable, check out the Bailey. They come in 13", 15", and 17". Even with a frame, you would come in under $3k if you bought a 13" or 15" new. Or, you can buy one used, as I did. There are always several people selling their machines/frames on the Bailey Yahoo Group.
Keep in mind that the Bailey is very much a no-frills machine; I find that it works great for pantographs, and there are plenty of people on the Yahoo Group that are doing much more complicated things with it. It just requires some patience and a certain amount of time put in for practicing :)