If you've never used Linux before, I would suggest you install it to another machine and learn the basics of installing, managing packages, using the command line, setting permissions, etc. before you set up a public machine running multiple network services. That sounds like you're asking for trouble, or at least frustration.
agreed.
i'd recommend debian for any non-desktop machine.
i use exim for mail, simple and easy to use, works great for me. the only problem i have with exim is that it was hard to find info on how to set up a catch-all (i.e. mail thats addressed to a non-existant local user gets redirected to another specified user). i finally found out how here under section 10.3.2:
http://qref.sourceforge.net/Debian/reference/ch-gateway.fi.html
apache is easy. just keep it up to date.
dns...now thats not going to be simple. either read up ALOT on bind (it is *not* simple) or use the kinda freakily authored and licensed djbdns (even then i'm sure you'd need to do quite a bit of reading, i dont know exactly how much easier it is than bind, i've never used it. and i like bind now that i'm used to editing zone files and whatnot

).
also if you use bind, make sure you keep it up to date, bind 9 is recommended, it was rewritten from scratch and is much more secure than 4 or 8. also chrooting it is a good idea (i recently re-setup bind and especially considering the most recent vuln. i decided instead of using debian's bind, i'd build my own bind 9 and chroot it, it's working great.)