Crossposted to rec.crafts.woodturning as well, which is probably a better newsgroup to ask in.
What are you trying to do ? Do some turning, or _learn_ to turn ?
You can make useful turnings on almost anything. I've made chairs on a pole lathe made in a woodland from a bendy sapling, and a chisel forged from leafspring. It's not a good way to learn though - so if you can do, try and find a course somewhere. You get a reliable lathe that already works and will do anything you ask of it. Then you can see about affording a lathe of your own, that's enough for what you want yourself. A bowl turner wants one thing, a pen turner another, and a furniture maker needs something long enough to take that table leg or chair post.
There are several useful brand-new lathes in the $250 region, with good features like variable speed, swivelling heads, cast iron beds, their own stands and decent bed length. As always, there are even better deals around S/H. $25 might even get you something usable. Half-a-dozen chisels wil get you started. You'll also need a few accessories, like lathe centres, a faceplate, sanding and finishing materials, and a grinder for sharpening. I don't regard a dust mask as essential for much turning (although some timber and any spalted timber does need it), but I do think a full-face faceshield is.
Other important tools are a big crosscut saw (maybe a chainsaw), axes, mallets, wedges and a froe. If you're learning, you need a large stack of green timber to practice on. You can't afford to buy this, so you have to scrounge it from tree felling work. If you live outside Arizona there's a lot of this going on, so so long as you can turn a log into something small enough to chuck in the lathe, you've a free source of wood. You might even have a woodstove to use up the remnants.
Don't learn to turn on expensive wood. Turning needs to "flow" naturally, so if you make a mess of something it's often best to throw it away and start again. If that timber cost you money, you won't do that.