After reading your reply I went back to the NJ MVS site for some answers. Not sure if I got everything needed.
Engine size is a personal preference. If it were me, I would have a 50 cc 4 stroke motor to keep it as a moped in order to avoid paying the premiums attached to a bike classed as a motorcycle.
Regarding not registering the bike and cutting off the motor when you spotted a police officer, it's just my opinion that it's not worth it. Once the officer spots you on a bike with a motor I would think the first thing he is immediately going to do is look for: moped license plate on rear of bike-helmet on top of head-goggles on face. And God forbid if you hit someone or someone hits you. The legal issues to follow will be more costly to you then the price of registering and insuring your bike. Remember, we live in NJ!!!!!!
I was having a problem trying to find clarification on the NJ MVS site regarding homebuilt bikes. It's my opinion Mariano that before you go any further with your project that you contact the NJ MVS and see what they have to say in regards to obtaining a title for your bike. Like I said, I'm just not seeing anything on their site that I can pass onto you. Let me know what you find out.
I like the cruiser bike idea. It's got that Whizzer vibe to it and should look really good once complete. I'd like to see it when she's done. Sorry I couldn't give you definitive answers...let me know what the MVS tells you.