With modest hardware, I do need to ask is there something specific requiring virtualization? It would be much faster running both servers on the metal.
If you decide to go with virt, TC can be the host; so far there's only Qemu available as an extension though.
Qemu is pretty simple to use, here's how to run the latest iso, while setting ram to 256mb, and enabling access to port 80 (web server):
qemu -cdrom /path/to/tinycore_2.0rc4.iso -m 256 -redir tcp:80::80
This redirects your host machine's port 80 to the virtual machine, allowing it be a web server in your lan.
Since Qemu uses the shared memory for its RAM, you might need to up the max limit (the default is half your ram):
sudo mount /dev/shm -o remount,size=1024M