Basically there's two kinds of bindings: Dynafit-compatible (sometimes called "Tech"), and most other bindings. Most other bindings will take any "standard" Alpine Touring boot. Dynafit requires a boot with special metal fixtures. Most modern boots are Dynafit-compatible (but you have to check, if you want that).
Then after you purchase skis with a binding on them, some expert needs to adjust the binding to fit your boots correctly. The binding has a limited range of adjustment (tends to be smaller range on Dynafit-compatible), so it might not be possible to adjust the binding to fit. So need to check this size compatibility before you purchase both binding and boots.