The SGI O2 has a standard VGA port, but when I connect it to a CRT computer monitor, I do not get a signal. Do I need a specific kind of monitor in order to use the O2?
It needs to be sync-on-green capable (any good monitor should have this mentioned in the specs).
But even then you may have issues, I have a few O2's and I have observed that sometimes one of my monitors (Dell U2410, SOG capable) really distorts the colors (towards green), replugging the cable solves the issue. I had no issues with an Octane with 13W3->VGA cable.
There are devices on the market that can help, called sync stripper - such device could remove the sync signal from green channel and put it on the regular VGA sync line, but it might be cheaper to buy an old 15-17 inch monitor that supports SOG by default. (O2 won't do anything more than 1600x1200 without extreme tweaks anyway).