This may be a bit of a noob question, but as I can't find the details elsewhere, it's up to you.

I have been setting up a webserver on my home machine, with apache2 php5 mysql and ssl, running on FC3 (ok, not ideal dist, but i like it). I am keen to find out how to set it up into a professional looking server, although the spec. leaves a bit to be desired. I know where to get apache2, php5, mysql, and OpenSSL, but I would like to know which is a good FTP server program to use, that lets each user log into a directory tree within the htdocs folder that belongs to them (i.e. multiple sites on one server). Also, could someone advise what is the best way to set up this "professional" server: i.e. there's plenty of tutorials out there to set up a few programs to work together, but I would like a suggested order to set them up in, and where to install them to on the disk.

What security issues are there to ensure remote access ONLY views what I intend, and not anything else?

Check out vsftpd for your ftp server. It looks like quite a few pro sites use it. It's also the default on Redhat EL and Fedora. Maybe you need to get a good Linux networking book, it maybe helpful to you.