Select the "High Quality" Setting
When creating an album on your browser, make sure to click the "High Quality" button you'll see under "More Options" on the left-hand side of the screen. That way, all the photos you'll upload will be stored in the Facebook servers at a higher compression sizes.
Only Use Suggested Photo Sizes
According to guidelines from Facebook itself, there are several "supported" photo sizes: 720px, 960px, 2048px (all listed by width). If you can get your .jpgs to one of those sizes, you'll be good to go with minimal compression issues. For profile pictures, you'll probably want to go with the highest size, 2048px (just note that Facebook also advises to only upload with the "High Quality" setting selected with this size).