A small jointer, 4" or 6", typically will straighten an edge or flatten a surface. There are many other ways to straighten an edge...table saw, router with a guide, router table and handplane.
Flattening a surface is best done with a jointer, but a handplane can also be used.
Now why a bandsaw? A properly set up bandsaw, with a good resaw blade will slice as little as 1/16" off one surface, and when backed by a flat board against the fence can be used to true and flatten a board up to 8" or 10" wide. Then with minor planing or sanding to remove the saw marks, you now have a smooth board. It's like a straightening jig.
I've never had to do this because I have several jointers, but it never ceases to amaze me when I resaw a thin slice off and wide board perfectly true.
The bandsaw is a greatly under estimated and versatile machine. It's best for ripping thick stock with no kickback, and by tilting the table 7 degrees in either direction you can make dovetail joints. Of course it's the only machine that will cut curves of all radii in most materials. Resawing small logs is possible with a sled, which I have used to get great spalted maple from logs found along the roadside. I should admit also I have 4 bandsaws of various capacities from 10" to 18".
Each has it's own application. I got a very capable used 14" Craftsman from Craig's List for $250.00, so don't assume new is the only way to go.