I wouldn't add anything to a basement ceiling. Basements typically have low ceiling and adding anything to it will just make it feel even lower.

IMO a wood ceiling in a basement is not a good choice I think wood ceilings look best in vaulted designs and there is no cheap way to really get that look unless you just want beadboard painted which really is not what you are looking for.

Lowe's and other bb stores sell beadboard panels. I used them in the ceiling of bedrooms in a rental property I owned. Looked fine. Be sure you have a plan for the junctures where they butt next to one another. Some kind of trim piece might work. I had a good carpenter and painter who just feathered them together with caulk and painted them white.

See painted that is not the look they want.

The panels do come unfinished or primed; I wanted mine painted white but that doesn't have to be done. and I wasn't suggesting it for this application, just a cheaper way to do what the OP requested.