VPN capability, either Cisco or Microsoft VPN client. Preferably MS.
Glad you prefer the MS VPN. I have enough trouble making the Cisco IPSEC stuff work with Cisco clients. :)
PPTP is the protocol that MS uses in their VPN. Anything compliant with that'll work. PopTop is the name of the PPTP VPN server in Linux, pretty sure there's a good client out there but I don't know the name.
MSTSC/RDP connectivity
rdesktop is the application you'll want. I used to run it on Linux all the time and fired it up just last night to connect to Windows 2003 Server. Works like a champ.
Toad for SQL work
The app from Quest? Pretty sure that's Java based, should run fine on any Linux distribution once you get a JRE on it.
Maybe VMWare or Xen... which would run off an external disk device if necessary.
I ran VMWare on Linux for years. They offer a basic 'player' version now for free that you could try out. Xen recently announced it was going to be free in basic form too.
Can anyone comment on the above and a linux distro that'll get the job done with an eee-1000 with either 1 or 2GB RAM?
Half the stuff you're looking for (Toad, VMWare) is going to come outside the package management system, so I wouldn't worry about the distro too much. A JRE, rdesktop, and PPTP client are so basic that anybody should have them. Ubuntu is where I'd start.