I've used strap bindings and K2 Clicker bindings (the latter of which I have now). The Clickers are nice because you can be clicked in and going down the hill before people with strap bindings are ready. One thing I do not like about the Clickers is that in packy snow I have to clean my boots and bindings of packed snow, also if you're in powder it's going to be more difficult to click in.
Other than that issue, I have no major issues with the bindings and have been using them for six years. The boots are a little more uncomfortable than regular binding boots (since there's no bindings to support your feet), but then again I have some old boots and I bet there's newer and more comfortable ones out. As far as riding style, I ride 80% freestyle and hit table tops and rails and whatnot... never had problems with my Clickers doing any of that.
Hope that helps ya with bindings. As far as boards, any board I've rode has been fine and that's been two K2s, a Division 23, and a Type A. Just make sure you don't get a real cheap P.O.S. and that it matches with what style you ride and your height and weight.
EDIT: Now that I think of it, that Type A started delaminating after awhile. It was my brother's board... nice ride but poor construction I suppose.