I just blew a capacitor. Now what?

I don't think the electrolyte is particularly nasty stuff. Electrolytics have been in use for about 80 years now (and failing!) and I've not heard of any major health scares, so I'd suggest you're OK with basic precautions - use rubber gloves getting it off, and wash those PCBs with flux cleaner to be on the safe side.

One place I worked sent a not exactly glowing report to a PSU manufacturer, with a footnote that the brown stains on the cover were from their reservoir cap, which "failed" in similar fashion, right after the report was printed.

I recommend resistance measurements on the bridge rectifier, in case any of the diodes failed short-circuit (the cap may have short circuited briefly, stressing the bridge), but everything else should be OK. And as the bridge has passed your tests I wouldn't bother replacing it.

As these look like home etched boards, I suspect the difficulty making resistance measurements may simply be the original photo-resist;if pin to pin measurements are OK, that's what matters. Look at the PCB in a year or so : if the copper is bright green and corroded, I was wrong...

After you clean the PCB using Brian's instructions, replace the cap with a 25v rating (not 16v). Also, use a 12v AC source (not 18vAC). If the PCB does not works fine, then replace the bridge rectifier, also. Most likely the other parts were not damaged, but if they were, replace them as needed.