$100 or less will probably not get you a tape machine at all, possibly an old reel-to-reel 1/4" two track deck. it will get you a low-end tascam cassette four track. that will get you the cheapest and crummiest of cassette four track machines. you might need to save up a little while longer if you want to get something that isn't the cheapest piece of crap out there.
You are going to have to widen your wallet a little more, but you should be able to get a 4 track TEAC (tascam) reel to reel on ebay for around $200. this is not a good machine (if you feel dumb asking, you can tell it's a 4 track by how many VU meters it has). But if you want to learn the properties of tape etc. this is a good machine to fuck up on.
Oh, if you have any questions that you think sound dumb, PM me, I'd love to help.
Be forwarned: Recording costs a lot and doesn't pay well.
Well, although I was joking, Sye Mitchell recently offered me an MTR-90 at $3,000 with 11mil heads and 24 channels of Dolby SR thrown in there.
So if you want his number.....
If you want to be a recording engineer "for the money" you've chosen the wrong profession. As I mentioned before you can probably find a Tascam 4 track reel to reel on Ebay for around $200. That's your best bet on your budget.