Having moved a few times, it is best to keep the initial visit short. Just a quick introduction and hand over the goodies. Put it on a disposable plate so they are not required to bring it back if they are not the 'social' sort.

It would be best to do it a couple of days after the move in as they will be distracted and stressed on the actual move day. I would suggest late morning (i.e. morning tea time) when they would probably be ready for a break.

I would love to have you as a neighbour. Go for it! You may find a new friend!