Hi Todd, welcome to the forum. You're story is very close to mine a few years back. I hadn't had a reel to reel machine since the early eighties when I was given. I found some 1/4 track tapes at a used record store (I was listening to vinyl almost exclusively at the time) and I couldn't believe the richness of the sound. I asked around a lot and almost everyone discouraged me from pursuing open reel as a viable format. Luckily I'm pretty hard headed and started buying other machines and tearing them apart to see what could be done to improve the awful playback electronics in most of them. Knowing that all my favorite records had been produced and mastered on tape told me that, just like the tremendous strides of record playback in the last 15 years or so, there was gold hidden in those tapes. If you look at those spec's that Ben listed, you can see that on paper, tape doesn't seem to have much going for it. But as you've heard for yourself, the spec's don't tell the whole story.
Fast forward to just about 2 years ago,.. Doc started hinting at the formation of the Tape Project.
I can relate to your hesitation to dive in with both feet (I too have very modest means) and Doc has made and excellent suggestion about getting an Otari. Due to the abundance of them on the used market, it isn't too tough to get a nice machine for a few hundred that is really worth investing some time to get running up to spec. It does take patience to find a good deal on a well cared for machine but the extra shopping around really pays off in the long run. I suggest looking at a few locally first to see what your looking for (Craigs list) and if you're near a large city, that usually isn't that tough.
Taking the time to learn about your machine can save you plenty too. In many ways, they're much more like working on a car than a piece of electronics gear. And while there are some specialized pieces of test equipment that you'd need, they can usually be had for crazy cheap prices on eBay. I really enjoy working on my Technics and over the years, the improvements in sound have been very gratifying.
If you do decide to invest in even one or two of the Tape Project tapes, be aware that the runs of a given title are limited so contacting the management directly may become important.