You can install on an old laptop (which may have a now unsupported OS), but then you need to fiddle with your router / firewall settings to be able to access from the outside.
The simplest to experiment is Linode.com You pay by the hour, so I suggest you try it for a few hours and report back here. Oh yeah, and USD$10 for Zarafa (it's AGPL but it's a contribution to help with the packaging). If at the end you decide you don't like it, it will have cost you a few hours and 11 dollars ;-)
Ready to splurge for a new domain name?
To make it even simpler, get your domain name from ClearCenter.com and then, even this aspect is all nicely integrated in the GUI!
ClearOS is super easy to install and makes it super easy to install apps.
Installing a LAMP stack is all in the GUI:
Installing OpenLDAP and Zarafa is also a point & click thing.
Installing Tiki & Prosody still requires a few copy-pasting in the command line, but it will also become a point & click thing later on.
It's all documented here: http://suite.tiki.org/Tiki+Suite+Install
There is one issue with Apache Rewrite Rules on a default install. It doesn't stop you from using Tiki. It just prevents Clean URLs unless you go and activate manually via a config file edit. This should be resolved for ClearOS 6.6