Yup, having the logo in vector format would be suitable for any kind of printing done. Giving the physical product would be beneficial but even just a scanned copy of the logo would work (I did this for my logo).
I would probably tend to agree with the vector route although JPG can work quite well too. I have done quite extensive photo and graphic design work of my own in Photoshop CS3,4 & 5 over the years (no sorry, I'm not trying to sell my services here - there's no way I'm as good as the pros) and I think one way to try to explain it is as follows:-
Generally, when you scan an image, save it as a JPG it will be a pixel based image - if you were to zoom in really close all you would see is a series of stepped, square-edged pixels giving an impression of the overall shape. The same would be true if you were to draw a shape in PS via a graphics pad.
Vectors, however, represent a real coherent line that truly represents the actual shape. You can also scale vectors, up and down as much as you want - the information will always be the same. Scaling jpg images in a similar way degrades them just a little bit more each time - and even more so when saved (JPG is a compression format and compresses it more at each save - each compression loses some element of information).
So vector illustrations will probably give you the most flexible format and the smoothest lines. I don't think you can save images in PS as vectors - the best package for this would probably be Adobe Illustrator.
However, it can depend on the final use for a logo. A logo on a business cards or greetings card is going to be quite limited in size by its very nature so you would be okay with a JPG file. Likewise on letterheads and so on. We too produce our own (photographic) greetings cards for sale in our own shop and print our logo and other info on the back. We've even scaled up our JPG logo to A3 width without too much degradation before now. For all these uses we use an 84kb JPG image of our logo on all of these and scale up no problem. But anything else it might be worth considering using a vector format.
If you go for a pro-printer, they may each have their own preferred formats (TIFF, png or PSD for example) so it's worth checking with them as well.
Now comes the rub - Cost. If you don't already have a copy of PS or Illustrator - it might be worth considering giving the hard copy calligraphy to a pro. Depending on which version you go for, PS/Illustrator could cost you anything between £400-800 each. I'm sure using a pro would be much much cheaper. On the other hand, if you see yourself doing a lot of different design work then it might be worth buying and teaching yourself to get proficient. And don't forget that all Adobe products within the CS (Creative Suite) range, as are PS and Illustrator, can 'talk' to each other - there's no problems with file compatibility between them.
There is so much more that can be done on Illustrator that can't be done in PS it's been on my wishlist for sometime now (take a look at
www.deviantart.com and search for Photoshop Brushes - a lot of which are made using Illustrator). But I've never been able to justify the cost against the benefit that it may give my essentially retail business, and to branch out into graphic design would be a whole new ball game.
Hope this helps. (But if I've told you how to suck eggs then I apologize).
I have made few before I got the one that I think looked right. But still not sure if its good enough to be a company logo 
