I use a LAMP setup with WHM, Virtuozzo, and cPanel.
I don't think that hes ready for whm and cpanel yet

i think its best he learn how to first use Apache and how to create your virtual hosts first (my opinion)
Anyhow onto answering more questions for you

okay so Apache is a http server program you can learn more about it here
http://httpd.apache.org/ os I like is Linux for hosting and distrobution wise i like Debian personally though some people would yell at me for that lol. Really its up to personal preference
i enjoy the fact that Debian has apt-get in it so if i where to want to install say proftpd i could just say apt-get install proftpd. Also with regards to linux servers
i never install a gui just use straight command line. Putty and ssh are your biggest friend. Also you may want to read
http://www.howtoforge.org/perfect-server-debian-lenny-ispconfig3 as it will help you though not everything would you want to use. The other thing is you are going to want to decide how you are going to do things.
In theory you could use a spare pc and slap Debian or Redhat on it and play around with it. The other thing you can do is rent a dedicated server and learn using this
although most dedicated servers they will set everything up for you on the start.
As for mysql you are right it is a database server and understanding the basics of networking especially ports and how to assign static ip addresses as you don't want your
web server changing addresses on you as it will become unreachable.
Now the thing is this all gets easier once you add whm and cpanel into the mix as it automates stuff for you or if you add ispconfig or some other control panel
the problem with control panels though and automating stuff is that if it breaks you always want to know how to fix it manually because stuff can go wrong.
Well i looked at this and realized noware i talked about virtual hosts X_X a virtual host is a way to have multiple sites on 1 server you will want to look at this link
to help you as i suck at explaining virtual hosts.
http://onlamp.com/pub/a/apache/2003/07/24/vhosts.html