After you resize with Paint Shop Pro, go to

effects > sharpen > sharpen

and sharpen it once or twice. DON'T use "sharpen more" because that usually OVER sharpens it. Well I mean use it if you'd like.

Also MAKE SURE when you are saving as a .jpg click the "options" button on the "save as" screen and make sure the compression rate is a low number, 10 or less.