As I'm clearly new to this, do I understand that kamado is the type, of which BGE is a brand of, or is BGE a variant or something different entirely?

Whichever direction I end up going in, I figure I should be able to get something decent at or below $1500 or so.

I'm hoping to find something that I don't have to babysit - I have 3 kids age 5 and under, so there's enough of that going on around here as-is.