Hi LCatGa (btw, we use our real names here,.. please read the Forum Rules at the top of the index),
There are several machines that have come to be favored by our members here. Many can be very reasonable for the basic machine. Probably the best value IMHO are the Otari 5050's. The Technics RS1500 series (1500,1506 and 1520) are also very nice machines but popularity has increased the asking prices to about twice the Otari's.
Be aware that most of us use these machines as transport only and employ outboard electronics, for playback.
Bottlehead offers a range of outboard electronics and there are currently 3 other solutions offered by other manufacturers (Doshi Audio, KingCello, deHavilland).
To use these "outboard" preamps (very similar to a phono stage), the stock machines will need simple modifications to bypass their internal electronics. Most anyone with basic soldering skills and electronic knowledge can perform these mods.
There are also a couple of "one box" solutions. The United Audio and Sonorus modified decks. These are ground up rebuilds of pro-sumer machines and while I don't have very much experience with them, I know Arian Jensen who builds the Sororus and I trust that his machines are quite nice.
Also, if you have the space and budget, the big studio machines are the way to go. Machines like the Ampex ATR 100 series or Studer master recorders (820,A80) are what all of use should be aspiring to but I don't really recommend this path for novices.
If you check out the Tape Project's home page, there is excellent info and pictures of what is currently recommended.
http://www.tapeproject.com/There is more info regarding other machines in the Tape Machine Compatibility Database which can be found at the top of the Reel to Reel Tape Machines forum.
Another good reference source is the "Beginners Guide" located in a sticky in the General Forum. It will help you to understand the different elements of magnetic tape playback and help you in your search for a good used machine.
I recommend that for pure novices to tape, you shop around in your area (maybe through Craigslist) so you can look at a couple of machines, have the sellers run it through it's paces for you but not buy the first one you see. Of course you may get lucky and look at a "minty" machine right off the bat, but without some depth of experience, you won't realize if a machine is running sluggishly or if it's behavior is erratic.
You should also try and find a local tech who has experience with working on reel to reel machines (they are getting harder to find). If you find a local machine that seems good, it would be worth it to take the machine for a quick check before buying.
If you do buy that machine (or if you buy one that isn't local) have the tech go through and do any regular maintenance and have the head adjustments checked. Much of this requires special test tapes and test gear.
Having a pro go over your machine is invaluable since it gives you a baseline for how the machine should perform.
This is a pretty deep subject and everyone's priorities are different so spend some time checking out and searching for info here before making up your mind.
Hope this helps.