I'm new to training with weights. Right now, my total fitness equipment invintory includes:
A recumbent exercise bike
two 15lb dumbbells.

I don't belong to a gym (and I prefer it that way), so I won't have a spotter available. Should I consider freeweights, or should I look for a machine?

Budget is important, so I'll be buying used stuff from craigslist or ebay.

You can probably pick up a cheap old weights bench and barbell for not much - if you're just starting out you should probably stick to safe exercises, i.e. those where you can't drop the bar on yourself (no bench press, unless you're really confident!).

Try a Total Gym. They are sold at most Sport Mart type stores.

My husband uses one. Your body weight is the resistance.

He also has a variety of dumb bells. 15 20 25lbs.

My husband and I use dumbbells (in weights from 3 pounds --for rehab -- to 25 pounds). We also have strap-on ankle weights with inserts that can go up to 20 pounds for each ankle.

We do Miriam Nelson's Strong Women program, which has a good mix of exercises and is a high-intensity, super-slow weight lifting program designed to increase muscle and bone mass.

@Dan: I work out at home as well, in a studio apartment. PowerBlocks are real space-savers.

A good barbell and weight set, some dumbells, and a basic bench can be had second-hand for well under $100 I think. Look for students selling old equipment at term end, weight-lifters outgrowing old sets and moving on, and spring cleaners.

I outgrew the meager set of dumbells I had very quickly. A sturdy barbell and a versatile set of plates would probably go farther.

Cost was also a prohibiting factor for me -- I didn't join a gym until several years after grad school. Ironically, a lot of trainers I've met eventually move back to a home gym because the gym they work at just doesn't fit their needs anymore.

John Stone has documented his home gym progression very well and has pictures. Worth a read -- especially his comments about getting a sturdy and properly rated bench.