I am new to the Linux server spectrum and I need a little help choosing some base options/features. I just got a laptop and I am hoping to convert my old desktop to a server. This machine is a

P4 2.8 GHz with HyperThreading
1GB of RAM
NVidia GeForceFX
120 GB SATA HD
60 GB EIDE HD
10/100 Ethernet

I hope to use this machine for file sharing (music, movies, documents, etc...)
If possible I would like to be able to sync my user folder with my Windows Laptop for backup purposes
It would also be nice to use it as a services server (DHCP, WINS, etc) to take the load off of the wireless router.
Another function that I like from a previous linux box is remote management through the VNC web client, except this time it would be nice to go through SSH.
The last function is a Web server

My main concern is what software I will need...
For my research I am sure that I will need Apache and Samba.
I noticed that LAMP is a popular server setup, but I am unsure about what it does. For example, with these services would I be using things like MySQL or PHP?

As far as distros go I was going to using kubuntu dapper if I need the LAMP feature or if not I was going to use White Box, because it is like the popular RHEL, without the subscription fees. However, if there is a distro that would work better for these services I am open to any of them...

Ok. Based on what your needs, here's what you could do:

File Sharing: Use Samba to share files with Windows, OS X, and Linux based clients. You can keep files in sync with various computers by having them mount the drive or by having them run rsync to the main file server on startup and shutdown.

Web Server: Use Apache. Linux, Apache, MySQL, and PHP (LAMP) will provide this, although if you're not using PHP or MySQL there's no need to install the entire LAMP suite. Ubuntu server edition provides a LAMP installer by default.

DHCP: ISC DHCPD3

DNS: BIND 9

WINS: Samba provides a mechanism for WINS serving, although it's not the easiest to set up. I don't know of any Linux alternatives.

If your concern in setting up DHCP/DNS on this is to take load off of your wireless router, you don't need to bother. DNS and DHCP are extraordinarily low-powered tasks. Setting all of this up is fairly straightforward, the hardest part would be setting up synchronization of various directories on different computers. Nearly every Linux distribution comes with SSHd (SSH server) installed by default listening on port 22 (the SSH default), so that's not any extra effort for you.
I'd recommend using Ubuntu Server or Debian Stable for a project like this. Ubuntu Server is more user-friendly than Debian, although it doesn't have the same proven track record. If you intend to use this as a server, don't even bother installing a GUI - it'll just waste resources.

Im not an expert but yes you would need SAMBA to hook up your server and the laptop and APACHE to set up you web pages sharing. Im not sure what DHCP server you could use but you could probably google for one. Wins servers are problably handled by SAMBA. VNC client it's kind of a pain to install and I believe you could start better off installing freenx instead. VNC I believe you have to re do you X installation and patch it up before get it to work. I have installed Cygwin in my windows machine, it is an X server for windows so I can just export my debian display to the windows computer, it works well to me but other guys say that freenx is a better option. I have absolutely no idea what LAMP is but I will check it out. Good luck.