Neil,
It's not the "BEST", but if you are running Windows XP or later (I think?), the operating system has a zip capability built in.
Using an explorer window like "My Pictures", highlight or select the pictures you want to "zip" or compress, then right-click to open a windows "action palette". Then move your cursor over the "send to" line and hold it for a second or two. This will cause a window to expand and then select the line "Compressed (zipped) Folder". A compressed file will be created in the same folder with the same name as the file that the cursor was over when you made the selection. You can also "drag and drop" pictures into a "Compressed (zipped) Folder" that you previously created or someone sent to you. See the picture below.
Now if the pictures are ".jpg" or JPEG files, they are already compressed some. You will need to use the above mentioned WinRar to compress a large number of JPEGs.
I hope this isn't too complicated?
There's also the option of copying the pictures onto a CD and mailing them...