I found out long ago that there's really no such thing as "unlimited" web hosting. If you actually plan to use many Gigabytes of bandwidth, you won't last long on an "unlimited bandwidth" web host. That's because they all have clauses in the contract that allow them to cancel your account for whatever reason.
Who they're after are those that use very little resources but are attracted to the idea of unlimited web hosting.
So you'd do fine with them if you're new to hosting. Or you could just go with a more honest host to start off with.