Welcome to the forums!
The short answer to your question is that any of the major Linux distributions will meet your needs very well. The 3 distros you name (Debian, Ubuntu, Slackware) are all highly regarded as Apache/MySQL servers.
The various distros are more alike than different, therefore most skills you learn with one distro will easily transfer to other distros you may use in the future. Therefore, all other factors being equal, I recommend you base your decision on the educational resources available to you. What teachers, mentors, books, courses, web communities, etc. will you rely upon as you learn the ins and outs of Linux? If your teachers/colleagues/friends use a particular distribution, then there is a strong argument for using that same distribution yourself.
If your plan is to use linuxquestions.org as your primary resource, then there's a strong argument for Slackware as this is a Slackware-centric forum. You'll find active Ubuntu and Debian communities at ubuntuforms.org and forums.debian.net respectively. I'd suggest visiting those sites to get a sense of the user community and evaluate where you think you'll "fit in" the best. This, to me, is as important as any technical considerations. Good luck!