If you're doing ballroom, latin and swing then you should probably just get a pair of regular men's dance shoes. Showtime has many different brands. For breathability and durabilty get the regular leather ones, not the black cloth ones and definitely not the patent leather ones (those are generally only for ballroom competition).
Latin shoes are a lot like regular ballroom shoes, except they have higher heels. It's easier to dance latin in ballroom shoes than it is to dance ballroom in latin shoes, so if you get ballroom shoes you can do both. And you can dance swing in them, too.
I do not reccommend the dance sneakers at all. They are good if you are doing hip hop, or if you are injured and can't wear your regular dance shoes for a short period of time.
Laura