Bring oil, lots of oil. Drive around town for a bit before leaving, preferably at both city and interstate speeds, then grab a bite to eat and look for any leaks afterwards. If you're leaking anything you should think about having a mechanic look it over before you leave. And of course buy a jug of whatever is leaking before you head out. Maybe also have an auto parts store check your alternator before you leave as well.

Good luck and welcome to the family!