If the weather is real hot, going ahead and get a vented textile jacket. They will not protect you as well as a leather jacket, but ultimately you are riding around on a small displacement vehicle so i wouldn't expect to crash at high speeds. make sure the the armor included in the jacket is CE rated, just to ensure that it really does help you in case the worst happens. Full face helmets are the safest, but I dont see too many people riding around with full face helmets (or a jacket for that matter) on a vespa. Perhaps a modular helmet would be most practical for you, or at the very least, a 3/4 helmet. I would avoid the 1/2 helmet, lest' you are going for the harley look or you're just particularly fond of the Nazi SS.
Gloves... Definitely look into leather gloves, not a mesh or a mesh/leather hybrid. Your hands will slide when you fall, and typically you will rest most of your weight there on impact, so to keep those palms nice and... skin covered... invest in comfortable leather gloves.
Long pants are a must, jeans or riding pants preferably, and shoes that not only have torisonal rigidity, but that cover your ankle in case you slide after the accident. It seems like overkill, yes, and it becomes a pain in the *** to keep gearing up and down everytime you get off the bike, but you've pretty much covered all the bases you can as far as gear this way.
Make sure to take the MSF course, invest in health insurance, and learn proper riding and collision avoidance technique.
Ultimately, few people riding scooters will follow through with more than a helmet, if at all, but ultimately it is your life and you decide how you want to protect it. I'll be the first to admit that even with all this gear, there are plenty of times when i ride with just a T-shirt.
...and pants of course