That 4 gauge kit you ordered would be fine if you don't ever plan on running over 1kW, and you can find 1kW @ 2 ohm for under $200. But chances are you might want some more power down the road, and I myself would want more power on those subs anyways. In which case you should either return that kit and buy a real OFC 4 gauge kit from KnuKonceptz which will likely be good for at least 1500w, maybe more if it's efficient. OR, to be on the safe side and be certain you don't need new wire whenever you upgrade, get some quality CCA wire from wherever. KnuKonceptz would be my suggestion since they have it in stock, and it's top notch stuff. If you had a month or 2 to wait, I'd say get AudioTechnix. And it will work with whatever amp you get, you will likely just have to strip off some wire on the end to fit in the terminals. Or, if you desire, get some 0 to 4 gauge reducers.
None of this is "mandatory" for you to have a functional system. But if you want to get the most you can get out of those subs, it's what I'd recommend.