A tif (or tiff) file maintains all original pixels, but a jpg does not. A jpg file is a compressed version of a file and the level of compression determines the degree of quality. If you think you will ever do printing on a printing press, tif is definitely what you want.
However, tif files are very large and can eat up your hard drive. Normally, when an artist sends me a tif file, since I'm only doing images for the web, I'll resave it as a jpg with low compression (high quality) and still maintain the original size. Even at low compression, it makes a dramatic difference in the file size and because I've not changed the dimensions (if it came to me as 1870 pixels x 2570 pixels, it stays that way), I can later make whatever file I would would need for the web and there is not obvious loss of quality. But, again, for a printing press, keep a tif.
This site has great information:
http://www.scantips.com/
I must admit that at certain points, I don't even quite understand everything there.