For MSTSC, if you are behind a router, you'll need to set up port forwarding on port 3389. And since Screamyx hands out dynamic IPs, you might want to register at dyndns.org or some other dynamic DNS provider and get a domain name pointed to your comp at <name>.dyndns.org. Couple that with the dyndns service on your comp, and it'll always point to your current IP, no matter how many times it changes.

Your home PC just needs XP Pro and above for it to function. You might need to configure whatever firewall/antivirus you have for it to run.