Walking around Mt. Vesuvius' crater

I have been fascinated with Mt. Vesuvius since I was round 10 years old, and finally I had my chance to see it up close. During our trip to Naples we paired up the afternoon hike up with a morning visit to Herculaneum.
The crater of Mt. Vesuvius can be reached by taking a bus to the entrance of the park and hiking up the rest of the way for our around 30 minutes. Tickets to the park can be purchased online, and shuttle bus tickets can be purchased near the Ercolano Scavi circumvesuviana station. Public buses are also available and are less expensive but are less convenient for us given our schedule.
The way up is pretty steep and we passed people who were struggling with the slope. Good shoes with good traction will also help a lot since the trail has a lot of loose stones that could be slippery if wearing the wrong type of shoes.
The shuttle was scheduled to pick us back up in two hours, but the two hours are more than enough to do the climb, walk around the crater, and get back down to the entrance gate.