I say unless you want to learn by doing, go download
XAMPP I have installed Apache/PHP/MySql many times and everytime there is a different error to deal with/fix. I leared a lot, but lately, I just don't want to deal with that stuff, so I found XAMPP and installed and everything works outta the box, its actually quite awesome if you just want to get down to development.
If you don't want XAMPP, look at your mysql error log and it will tell you why its not starting, then google that error and you should find the solution