In terms of items that may be prohibited from being taken through airport security, you will have to find out from the individual airports GA section if this will apply to you. I have been waved through at some of the biggest airports, and sent through the metal detectors and had shoes removed etc. at some of the smaller ones. Prepare an overnight bag that does not have any sharps, liquids and you should be fine.
That's my experience too. They're not too worried that any prohibited items make it onto your aircraft, but they're worried that you might leave any prohibited items in the terminal, or give it to someone behind security who's going to be on a commercial flight.
So it depends on the exact layout of the terminal whether you can bring any contraband with you. If you have to cross the main public terminal to get to your plane you generally have a problem, but if there's a VIP terminal or direct entry onto the platform you are generally ok.
Best to be safe though and leave anything that might even remotely be considered contraband in the aircraft. It's hard to figure out the exact situation in advance.