Hi JunkYard
Welcome to the forum.
Your motherboard take a Pentium 4 which will have no problem running
Tinycore. The machine I'm writing this from has a Pentium 4.
You don't say how much RAM you have, but if you plan on running a
modern web browser (i.e. Firefox) , you'll want as much as you can
afford. That motherboard is rated for 3 Gbytes.
The 32GB HDD should be fine.
Your motherboard has a wired network connection, so I would recommend
one of the Tinycore ISOs, not the much larger CorePlus ISOs. Those are
needed if the only network connection available to you is wireless.