I use about 30 feet of plastic-coated elevator cable...you can't cut this stuff with bolt cutters, and the lock I use is a pin-across type that cannot be cut either.
I make sure to loop it through the rear wheel, around the frame, back through the front wheel, etc, to secure every piece someone might run off with...and find an object that cannot be hacksawed through quickly (which leaves out many signposts).
You can buy the cable at Home Depot, as well as the lock, and of course, anyone touching my moped is in for about the rudest "shock" of their life (Model Charge1K anyone ?) due to an additional security rig to keep their hands off.
For the ultra determined who might actually make off with it, there's also a radio beacon (off the same battery as the zapper) and I will come for my 'ped, and itchin to rocksalt someone in the process.
Having had 80% of the mopeds I've ever owned stolen or vandalized into oblivion, yeah, I can get pyschotic about it, sure....but my moped is MINE, and I intend that it stay that way.
Any mall personnel telling me I have chain it to the bicycle rack gets serious attitude from me right away, that's how my first moped was stolen, a nice 1984 Puch Austro, too....they unbolted the rack itself and heaved it into a truck.
As for U-locks, they do ok, cause most folks don't have an old volvo jack laying around, there's a trick to bustin em that way.
One thing to look out for is attempts to "ground" your moped so the thieves can come back later when less people are around and make off with it....ripping the ignition coil wire out seems to be an all time favorite...along with slashed tires.
Oh yah, and one last word of warning, cause I had this happen once....some assholes think it's funny to loosen your wheelbolts or disconnect your brake cables on your while you're shopping - before you get on yer ped, CHECK, or you might be sorry.
As for the helmet...no one would want mine, battered as it is, but on most occasions I just carry it with me.
People are pricks....
PS - My suggested method of handling "grounding" attempts is to linger nearby with a handy negotiation tool, such as a baseball bat, tire iron, etc - not only does word get around to stay AWAY from yer wheels, there's a personal satisfaction factor, and you might just get replacement cost out of it.