Well, there are analog machines around just about every budget right now and the market is down on them generally, so start with a budget and that will narrow things down for you. Then figure out how much effort you're willing to put into maintaining them (if any), and how much you're willing to spend on tape and supplies--tape gets more expensive as it gets bigger. You could get a big reel of 1/4" tape for 50 bucks or so, or 1" will be more like 150. As for brands, I would stick to new reels of tape so you only have two brands to look at--RMGI or ATR, and which you buy will depend some on the machine you get and some on your tastes. If you're thinking of a 4-track machine, you're most likely going to have your choice of 1/4" (semi-pro format) or 1/2" (pro format).
In addition to the machine, you will need some inexpensive cleaning supplies (a bottle of 99% isopropyl alcohol, about a dollar...a box of paper stick cotton swabs, a few dollars, and you probably already have some Windex or 409 around the house for the pinch roller). Depending whether you get a prosumer deck or a professional deck you may want/need a tension guage but cross that bridge when you get there. You probably want a basic multimeter handy too. As for a demagnetizer, it kind of also depends. I just bought a Han-D-Mag but I'm using a professional 1" MCI machine in a commercial studio so I did need that...occasional use in a home studio, I may not be so worried about it. In any even, I bought the Han-D-Mag from Markertek for about 60 bucks shipped.
In buying an analog machine possibly the most important thing to look at is the condition of the heads, beyond the Tascam cassette 4-track recorders, these machines are pretty much all "vintage" and only worth the heads that are on 'em. Here's a page showing you what a bad head might look like:
Audio Tape Recorder Heads that have gone BAD !!! Beyond that...in 4-track format, prosumer brands, you'll probably be looking at Tascam and Fostex (other guys here are much more well versed in those), professional brands you'll likely be looking at Otari (especially MX5050), MCI JH-110, possibly Ampex. As a newbie, I would avoid the MCI unless it's a stupidly good deal, it's in OK condition and you're feeling really adventurous...trust me, I'm a newbie who just spent over a year getting a 110 back in working condition. It was a mammoth pain in the ass (but a very cool machine). Ampex is gonna be pretty old, the flipside to that is pretty simple inside...generally you would expect the pro machines to need more maintenance...really if I were you, I'd look at Tascam, Fostex, Otari and avoid "fixer uppers".
