Server administration can be a great deal of fun, if you're into that sort of thing. But, I would definitely start with a good book and a local installation that won't cost you any cash for a reinstall. And of course, whenever you have a particular setup/installation question, Google knows the answer.
I'm kind of a simpleton and a slow learner. So, of course I have to recommend going the safer, slow learner's route ...
Find out what *nix flavor you'll be working with. I have two recommendations here:
FreeBSD: It's incredibly stable. FreeBSD systems tend to go years without needed a reboot. They're generally more of a pain to work with though, and since it's a BSD, your favorite commands tend to work slightly differently (paramters are required in different orders and so forth).
CentOS: It's probably the easiest nix to install and configure. First step after installation (or VPS purchase) is to install yum (if not already installed). From there, getting your LAMP stack working is cake.
Buy and skim through an administrator's guide to your choice.
Install a copy on a local computer (buy an old crappy PC for $25 to $100)
Walk through setting the server up, bookmarking and highlighting or writing notes for important steps along the way.
Get comfortable with the BASH shell, VIM, and the necessary config files.
Shell out for that VPS and pick up configuring where they left off (You'll probably have to configure the LAMP stack a little bit).
Bear in mind, if your'e not already somewhat familiar with the *nix command line, it can take awhile to learn--even for some of the more speedy learners. Most folks who confidently tap flawless command after command into the prompt have already spent months or years mistyping commands and accidentally destroying their systems despite the plethora of reference materials they have at their disposal.
Once you're confident working with your nix and you have your VPS ordered and ready, you'll be SSHing into your server with the ssh command on your local nix or OS X box, or Putty on your local Windows box. The most lightweight text editor I am aware of on *nix systems is VI/VIM. It's a bit of a challenge to get used to, but I highly recommend it for your configuration and on-server editing needs.
If you happen to choose CentOS, just remember that the easiest and best way to install software is with the yum package manager. Don't build thing from source unless you absolutely must! Additionally, don't start and stop services manually if you don't have to. Use the service command. And of course, when you've forgotten what parameters a command takes, check the manpage first! (man <command name>) If you don't even know what command you need, you can man a related command and look at the commands at the bottom of the page.
In terms of server monitoring ... if you think you'll need that kind of thing, two things to check out are Cacti and Nagios. Cacti will provide statistics about CPU usage, bandwidth, etc. Nagios allows you to monitor service statuses and send you emails or texts if a service goes down and needs attention. ... Cacti may be able to do that at this point too--I haven't done a fresh install in a long time.
Ok ... sorry for the long-windedness. I'm excited for ya ... should be a lot of fun.
Good luck, and have fun!