As detailed on http://www.mysql.com/products/database/
, there are quite a few MySql versions.
The community version is free. Download the current stable release.
v5 is definitely better than v4, thanks to support. Check out the details on mysql.com if you need to know the exact changes.
I recently upgraded from v4 to v5 too and it was a breaze, using mysqldump to dump the v4 database and then import it into the v5. Worked like a charm.
Details on apache can be found on apache.org. There are plenty sites with details on PhP and 4th and 5th version.
In general, compiling packages from source gives you more flexibility (ie you can set the options you need, define where the programs are compiled, etc), but it's harder if can be a little tricky at times. VB6 programming experience won't help you much with this, in my humble opinion.
Binary, pre-compiled, packages are easier to install, but don't offer all the flexibility.
If you want a standard LAMP server, I recommend sticking to installing from packages and only compiling from source if you really need to.
A lot of Linux sites offer how-to's, tutorials, and stuff like that. Examples are tldp.org and this site's tutorials.