The specifics of how to identify your wlan depends on which bus it's attached to. For an on-board WLAN card that would be PCI, or perhaps USB these days I guess. So get the lspci / lsusb (and lspci -v -v / lsusb -v -v) output and correlate that with the output from lsmod and you should be on your way. The startup messages in dmesg are also helpful although often somewhat cryptic; although certainly not more so than the lsmod driver names.

As for "bare-bones CLI-only" Linux, I am quite comfortable with Ubuntu as a front-end for the command line (and very little beyond the command line -- Emacs, and my browser, and my music player, and occasionally the photo viewer). If you really wanna go hardcore I guess you will be looking at Gentoo soon enough, though (-: