Running a web server isn't always as fun as it may seem :) Unfortunately, it does consume a hell of a lot of your time doing mundane routine mundane tasks.

I used to work for a dedicated server provider in the UK as a sys admin looking after some 450 servers and my daily task list went something like this:

1) check webserver, database server, mail server and general server logs for any errors / hack attempts / crashes / etc
2) Scan the relavant websites (php.net, mysql.com, etc) for updates to software and install / update them as nessacery (which usually involves spending 5 hours trying to get all the compiler flags correct for the modules you need :D)
3) Check server load to make sure nothing has hung and no processes are locked / crashed
4) Check the cron jobs (scheduled tasks) to ensure that they have run
5) Check the backups
6) etc...etc...etc... :)

If you just want to run 1 or more websites, I would fully recommend using a standard webhosting / reseller hosting account. The benifits of having a techie to do all your PHP / Apache / MySQL upgrades for you are priceless in my eyes :)

If you want to "try out" running a server before you decide to rent one, download yourself a copy of Linux (any brand of linux will do but Fedora is a popular free brand for servers) and install it on your own PC (duel-boot with Windows - most modern linux distributions can handle this without much trouble) and have a play.

One important thing to remember when you do this is that on a rented dedicated server it will all be command-line based - you won't have any fancy windows to point and click (well, unless you rent a Windows server of course :))

Alan.