A few comments:
-If we have sufficient time hanging around in the present to prepare, a lot of very useful pre-work can be done… ie, designing and working all of the kinks out of the most efficient black-powder-firing rifle ever, with special attention paid to easy of maintenance without access to very many tools. Instead of bringing back a wide variety of tanks, trucks, bicycles, helicopters, etc., a whole line of vehicles can be custom designed and built (remember, time and expense are no barrier) which share as many spare parts and maintenance items as possible. It’s going to be a lot easier to maintain a fleet of modernish vehicles if at least they use the same type of oil, the same size of ball bearing, etc.
-I expect that it’s possible to inoculate any time traveller against the prevailing diseases of 300 B.C., although doing the opposite might be nigh impossible. Will time travellers kick off the black plague?
-Modern domesticated plants and animals are far different from, and in many ways superior to, their ancient counterparts. Bring plenty of them.
-Your best bet, politically, is to pick a reasonably benevolent leader of the time and ally with him. Ideally, bring along a beautiful and charming young woman who’s willing to marry him, put up with 3rd century crap for a while, and slowly lead him by the nose towards modern liberal thought. Having the heirs to the throne of that kingdom raised by you in your schools won’t hurt your mid- to long- term prospects.
-Another interesting question is to what extent to you want to freely release information. Initially, at least, you might want to share some basic information about egineering, agriculture, hygiene, etc., with everyone who asks, establishing yourself as a benevolent presence, and raising the standard of life for everyone. But save enough of a high tech edge, or even a (by our standards) medium tech edge, that no one will be able to challenge you for dominance for quite some time.