There are lots of ways to do this. Are you going with the beta version of 2003 ? If yes, then I would suggest that you wait until the final release are out, or use Win2k Server.
To answer your questions:
1. Logging to central server
Do a dcpromo on your win2k server and make it a domain controller. This way your users can have a login server.
2. Access certain apps, not other apps
There is no easy way to do this. You need to be creative 🙂 For instance, you can lock the application w/ group policy and not allow your parents to / not to access certain apps. You can also lock down the desktop and start menu so that the only way they can start an application is from the desktop and start menu. You then custom make their desktop and start menu to show only their allowed applications.
NTFS security is also another way to restrict the app, although I wouldn't recommend it because it is a hassle.
3. If you want to give each person 2 GB of storage space, you'll also need to be creative. You might want to create a central storage on a file server where they will save their application. You can then use a login script or GPO to automatically attatch a network drive to their profile so that they can't save somewhere else. After making sure they can only save to a single location, you can now go to your file server and assign quota to your parents for 2GB.
Win2k Active directory is very strong and powerful. When correctly implemented, all the things that you want to do are very possible.
eRr