So I'm going to check out some old mountain bikes and road bikes with the intent of converting them to a single speed with freewheel hub. These bike won't have horizontal dropouts. What bike specs do I need to look for to assure that they're conversion compatible?

Also, is a chain whip and cassette lock ring tools absolutely necessary to complete the conversion???

Really you can convert anything to a singlespeed, even if that means using a chain tensioner.

most conversion kits require the hub to be a shimano, are there certain distinctions other than logo to identify if its is???

yah, hub splines are different on shimano hubs as they are to campangolo hubs.
check sheldonbrown.com to check the difference