Welcome to the world of Shifter bikes!! BTW, was it a Silver one off of Craigslist? Just curious since I'm constantly trolling ads for bikes for others and I just recently finished a "big" scooter purchase (in other words, a bike that runs that cost more than be budgeted

) so the current offerings in Phoenix are still fresh in my mind
As far as where to start: Engine first.
-Account for all parts
-Make sure it has compression. Many Stellas and Vespas get sold off because the bikes had a "soft seize" and have damage to the piston and cylinder.
-Sort out electrical first: You can test for spark with ease. It's either there, or it's not. Circuits don't need "adjusting". They either work or not and that makes troubleshooting easy.
-Then fuel. Start by cleaning out and/or rebuilding the carb. New seals, clean out the jets and new hoses are best. This is also a good time to make sure the oil injector system is working because without that, you'll frag everything else.
-Crankcase and clutch: Change the case oil (duh!), adjust and inspect the clutch and hardware. Check to see if the engine engages with plenty of room and there's space at the clutch cable arm.
-REPLACE ALL CABLES! It's honestly pretty easy (if not a bit time consuming at first) and a good idea if the bike's been sitting. Buy yourself a
Fourth Hand Tool by Prima. I cannot stress enough how awesome this tool is and how it makes cable replacement a breeze
-Inspect suspension and tires. Rubber is cheap and I strongly suggest splurging on the "expensive" types like Continential Zippy 1's or 3's or Michellin S83's. A good tire will never let you down and the factory Stella stuff just isn't up to snuff after you've ridden on good rubber. The extra 7 to 10 bucks is WELL worth it!
Bodywork can come later, and can be in all flavors. If you're interested in that, I've got some experience in DIY bike painting that doesn't require a paint booth, but is a step up from just krylon rattle can (it does require spray cans, but custom filled ones and there's a trick to it. Think of it as painting the "old school" way instead of the cheap way).
I learned how to work on shifter scooters on a Stella, and went from novice to having a TON of confidence in just a few years. They're great bikes if you take care of them right. If there's any more questions just ask around. There's some good minds on here. Also, our sister site Modern Vespa has a not-so-modern section, and most of all the articles on P-Series Vespas can be used to improve your Stella save for a few different bits.