So, I'm not an expert, just a user. You might try removing all files that have zero bytes. Some of these are needed to run your programs, so your computer will ask if you want to remove it and you can say "no" and continue.
If you do run the defrag program, it will reorganize your hard drive so your files are continuous rather than in different places. This will help with the speed. What your computer does when you change a file is put the change elsewhere on the drive rather than putting it all together. It remembers where everything is, but will run faster if the file is all in the same place. If you use your computer a lot and keep changing files, it might be useful to run this once a month.
Do you have a program installed that will remove spyware? That might help, too.
If your speed is a problem with the booting up process, maybe your computer is running programs in the background that you don't need. Also, if you have old files you no longer need, removing them will help, but you should do that before you defrag. I don't mess with compressing files unless I'm sending them to someone or writing them off onto portable storage.