Are we stuck with the grand company once we choose one?

[Colino]

Well it states you are "not yet bound" so it sounds like eventually we won't have an option to change companies

That's exactly what it says.

You get one (possibly more?) recruit quest per company, during which you can "try them out" and see which one you prefer.

The more advanced quests will ask you to pledge to one of them and that's pretty much what they've been saying since the start of the whole Grand Company tease.