I'm a professional photographer, but I'll try to put this in layman's terms and see if I can come up with some suggestions and valid decision trees. Note that you may have more than one good solution to your problem.
First, the image type question. There are two ways of reducing the file size, one is by reducing the number of pixels that the camera uses, and the other way is to use all the pixels but use a type of compression (JPEG) to make it smaller. USUALLY the best way to get a better image in a smaller package is to use JPEG compression.
With JPEG, you might lose a little bit of information in the extreme highlight and darker areas, but with modern technology it's not all that much. When I am shooting candid shots at weddings, unless the lighting is extreme I am perfectly confident using a mildly-compressed JPEG file. I doubt that a layman could tell the difference between a RAW or TIFF (common uncompressed) image file and a big JPEG, or even a mid-compression JPEG, if the resulting image was printed under 8 x 10 inches.
NOTE: Most cameras offer about three levels of JPEG compression.
SO-- to cut down on the amount of memory you will use, for most shots I recommend that you do NOT use TIFF or RAW, but JPEG. If you are not printing anything more than 8 x 10, there is a chance you can get away with using not the biggest JPEG setting but even the next one down. Run a test and see if you can tell the difference. Note that this will NOT cut down on the number of megapixels the camera will use to generate the picture.
For those once-in-a-lifetime shots, switch the camera over to TIFF, or RAW. RAW contains far more information and will result in better images. HOWEVER, RAW results in big files and sometimes requires special add-ons or software to process, so for you I wouldn't recommend it.
Frankly, I'd recommend using one of the little USB disc drives. I just picked up a 500 MB model from Costco for $105. You can use the drive later to transfer all of your personal files from your old computer to your new one, and you will find lots of uses for it after your trip.
Here is something your computer might allow. Try to take the images directly off of your camera or memory card, and put them directly onto the USB disc, without putting them on your computer's hard drive. That way, you can just dump all of your images onto the USB disc without worrying about storage space. Like one other respondent pointed out, to fill that up you'd have to shoot pictures almost constantly.
Other good choices are flash drives (take care not to lose them), or you could simply buy several 1GB memory cards for your camera and keep changing them. With my Nikon D2x, which is 12 MP, at medium JPEG I can fit hundreds of images on a 1GB card.
I hope I've been more helpful than confusing. But the main thing to take away is that you have several ways of doing what you want, all of them pretty effective. Have a great trip.
Bill C.
website:
www.williamcornett.com