Bill wrote:
I'd want a jointer, the table saw's companion.

Please help me understand this (newbe here). If I rip a board along a fence
on a table saw with a decent blade, I assume I'll end up with a pretty nice
cut. Will the jointer give me something "extra"?

Yup!

The jointer will straighten the edge that goes against the TS fence, as
well as set the edge to a perfect angle referenced from a face. If the
edge riding against the TS fence has a curve, or the board has a bow or
crook, the edge you'll get off the blade will be less accurate.

Also, properly prepared stock is far less likely to kick back.

A jointer will also flatten a face.