Read fred's post about moped repair/tuning for upkeep suggestions - it pretty much covers everything.
Gas wise, just the strictly normal stuff (extra additives might not be great for the moped in a worst case, and generally won't do anything good for it in the best case)
Oilwise I use the synthetic Redline oil (bit more but the moped seems to smoke less and generally I like it) but a two stroke engine oil will do in a pinch. Generally the mix should be anywhere from 43-50 to 1.
Helmetwise, any motorcycle shop should be able to set you up (I tend to shop up at McrBride cycle)
Legally you need insurance, shop around for that as you'll get WIDELY different quotes, registration, and plates. You don't need a used vehicle information kit, don't need a safety inspection, and don't need a clean air inspection. You need a license to ride, but any license will do (including car learners permit)
Costwise it won't be much - insurance should be (if you are a brand new driver) under 400 per year, and much less if you have any driving/insurance record. Plate stickers are 12 bucks a year, and when you register you'll have to pay tax on your moped if you didn't already pay tax on it (if you bought from a dealer for example and they charged you tax on it)
Aside from all that, be careful of streetcar tracks (not fun on a moped, trust me!) and enjoy your ride!