when i'm scanning from a scanner, i always save in .bmp. when scanning from a negative scanner, i always save in .tiff. this, as others have mentioned, is mostly for archiving. i rarely work in .tiff. i load the image in paintshop pro from the .tiff and then save as a .pspimage,
psp's proprietary format. i then do ALL my work in .pspimage. once done, if i'm loading to the web, i save a new copy in .jpg. if i'm printing, i print directly from .pspimage after merging the layers or from a copy merged layer.
so, file size is somewhat secondary... if you have the workspace/resources to do so. i've worked on 90 meg files before in
psp, but i admit it tends to get slow after a while and there's really no reason to do so unless you're printing in very large sizes. normal printing used to print at about 200 dpi. anything over that in file resolution wasnt worth doing. there was no appreciable gain in print quality. today, printers are getting better and better and i'd tend to want to save in 300 dpi for printing purposes, especially on print shop quality printers or for larger formats. normally, home printers go no larger than about 13 x 19. so, a 300 dpi resolution is fine for these. commercial printers, i'd ask how fine they can do and go with that.
so, if you're printing at 12 x 18 at 200 or 300 dpi, there's your formula, and that's going to dictate the file size. 12 times 300 = 3600. 18 times 300 = 5400. so, your image size is going to be 3600 x 5400, which is 19,440,000 bytes or approximately 19 megabytes. and that comes close to your 22 meg .tiff file. if you cut this down to 200 dpi, it would obviously be a bit smaller.
but, what you really might want to do is just run some comparison tests. save your image as a .jpg and save it as a .tiff. then simply test print both and compare the results. that's really the only thing that matters in all this and the only true way to find out for sure.