What is the best format for printing?

There is a lossless version of the JPEG image file format (it doesn't use JPEG compression), but it isn't implemented in much if any software, including Photoshop.  Even at the highest quality levels, JPEG compression causes some alteration in some pixels, but at the highest quality setting, the alteration will be very slight and should not be visible even in contrasty areas.

The downside of JPEG vs. PDF is that JPEG files cannot contain vectors, so all vector shapes, and more importantly all text, will be rasterized; PDF files can contain vector shapes and text fonts.  If the printing shop uses a RIP or a Postscript printer, the vector content will be printed at the printer's highest resolution, which will likely be higher than the resolution of the rasterized image.

Not to start an argument but I'll give my opinion.  Majority of my work is portraits and weddings.  As I work on files I save as psd's.  Once I'm POSITIVE I'm finished I save as jpgs, highest quality.  Those I save to CD and external hard-drive.  In the event that I need to do additional work on one of those jpg's, at a later date, I again work it as a psd until finished.  I then save it as a tif to avoid any further degrading of that file.

My point, right or wrong, is that I don't see any degrading of files saved once  at highest quality jpg.  That said, I never (never say never) save as a jpg twice.

Not enough information! Is this a local printer (one attached to your computer)? Are you sending it out to a printer?

If it's local and your printing from Photoshop,  the format doesn't matter. If your sending it out to a commercial printer, then the proper thing is to ask them what format they would like.

John