I've recently completed a Beige G3-ATX conversion while keeping the G3 logic board intact. I can't say the same for the ATX case though.... The case was $30 from TigerDirect's outlet store in Raleigh, NC and was the cheapest one they had with a removable motherboard tray wothout the huge holes in it.
Is there some sort of template for the I/O shield for the logic board? Currently I'm using the metal shielding from the inside of the original G3 desktop case. It works, but it does not look very good. That and the sharp edges.