I agree, any decent HD camera is good. Most cameras come with the cables to connect them to a TV set. You need a camera that can output via whatever format your monitor/TV accepts as input (for HD video that's usually HDMI these days).
Firewire is nice, but quickly becoming an outdated technology. Firewire was great to have on older cameras that record to tape or an internal hard drive because it allows HD video to transferred faster than you can with the older USB 2.0. I don't keep up on the specs for most newer consumer-grade cameras, but I suspect that most of the ones on the market today support USB 3.0 which is actually faster than firewire (usually cheaper too).
If the camera records to memory cards you definitely don't need Firewire, just stick the memory card in your computer.
Remember that whatever you use to transfer your video to a computer (memory cards, USB 3.0, Firewire, etc.) you need to be able to connect that to your computer. Most PCs have USB 2.0/3.0 ports and you can purchase a memory card reader inexpensively if one isn't built in to your machine. Macs usually have USB slots, memory card readers and firewire ports built in.
Personally, I wouldn't worry about using On Location for simple puppetry practice. It's expensive and unnecessary in my opinion.