I own a Jet 14" bandsaw and do not own a table saw. When buying tools, I decided to buy a bandsaw before a table saw. Now I may never purchase a table saw. What I like about a bandsaw:

• Quiet. A bandsaw is quiet compared to a table saw.
• Small. A bandsaw takes up much less floor space than a table saw.
• Versatile. Here are some of things you can do on a bandsaw: rip, resaw, cut small pieces without jigs, taper a table leg without a jig, saw a log into boards, cut tenons with only a fence, cut curves, and perform free hand cuts.
• Small kerf. Bandsaw blades are thinner than table saw blades, so you waste much less wood, particularly when ripping and resawing.
• Safer. Of course a bandsaw can injure the operator, but I feel it is much safer because you are less likely to have a catastrophic injury. For a comparison, read the WWA Accident Survey. In particular, a bandsaw will not kick back work at the operator like a table saw can. However, cutting a dowel on a bandsaw is very dangerous.

In general, a bandsaw is not good at dealing with sheet goods (plywood, MDF, etc.), but I really don't like using plywood, so that has worked out well.

Learning more

I recommend The Bandsaw Book by Lonnie Bird. Mark Duginske also has a book that many people recommend. I have read both and found Bird's book was much more straightforward. The bandsaw is a simple machine. There is no reason to complicate it.

Is "bandsaw" one word or two?

I have no idea! Delta uses two words in the name of their saws. Jet (and most everybody else) uses one word. The two spellings seem to be used interchangably. Keep that in mind when searching the internet.