Welcome to mac-land! This problem is not hard to solve... It does depend slightly on exactly which models of webcam you are using though.
Anyhow, in my case I use a c910 and a c920. The c910 i can use with the Logitech Webcam Software for mac (which i can use to record HD video with it, as well.) My c920 is not compatible with that software which is kinda lame, but whatever.
Photobooth and iMovie are both able to record videos, but they don't aaalways recognize logitech webcams. (make sure the webcam is plugged in BEFORE opening the program though, just in case.) However, in my case the built-in cam is pretty good, especially if there is ample light.
I'm unfamiliar with manycam because i found it clunky and the watermarks ugly as fuck so i never really used it. You will need to use Camtwist to make this work. I can't recommend that program enough honestly. It allows you to do picture-in-picture, it allows you to adjust your brightness and colour settings, it allows you to watermark , it allows you to force the camera to any resolution you wish (which can be very handy with widescreen cams that automatically set their own aspect ratios wrongly, lol.)
ANYHOW! The way i record videos while camming is simple, i use my c920 to cam on my camsite and i simply set either Photobooth, iMovie or the Logitech Webcam Software to record a video simultaneously with the other cam or the built-in cam.
When it comes to doing picture-in-picture, use this method.
Except obviously instead of the "livestream" software he uses as his base image, you use either photobooth or the logitech software or whatever. you don't even need to have them recording to do this, because they show a preview that you can use.
Anyhow, there you go. Allll the things. Camtwist does have a bit of a learning curve on it, sometimes it can be finicky to get it to show up as a source in every browser and the settings can be a pain to get right at first, but once you get them down you can just save them and pull them up every time automatically. Feel free to PM me if you have any trouble making that bitch work!
Good luck ^_^