Mt. Vesuvius

Hi,
You can take a bus from Pompei Circumvesuviana station or other near the amphitheater (but it could be difficult to find a stop there). Some stands sell tickets outside the railway station (Circumvesuviana) and you can't avoid them when you go out. When you arrive at the crater (about 40 minutes of bus) you can purchase the ticket for the entrance. I don't know how much it is today. There are 2 or 3 possibilities (a car, a bus, a “tram”). You pay only for the transportation (with the return — you HAVE TO take the same bus to return, they will tell you: we will wait for you here at this exact time), not the guide.

You need about 1 hour to get to the crater from the bus stop (1000 m asl).

The excavation site of Pompei is very interesting and there are different expositions and houses open to visits there now. You need more than one day to visit all the sites. I would advise you to see what is interesting for you and download the map of the site from the official website to plan where to go.
The second possibility is to visit the Forum and nearby areas. You can do it in 1-2 hours from the Pompei Circumvesuviana station.

Some additional data:

https://community.ricksteves.com/travel-forum/italy/pompeii-and-vesuvius-69e8366c-1e75-4a14-a0bc-0677269492d1

This is one of the buses, from Amphitheater:

From Pompeii to Vesuvius by bus
Connection service from Pompeii to Vesuvius offered by EAV Bus.
Duration: one hour
Ticket price: €2.70 one way. You can buy it on board.
Pompeii – Vesuvius opening times: every day at 8:00, 8:50, 9:40, 10:30, 11:20, 12:10, 13:00, 13:50, 14:40, 15:30
Pompeii-Vesuvius stops: Piazza Anfiteatro, P. Marino Inferiore motorway entrance, Torre del Greco motorway exit, Observatory, Chairlift Q.750mt, Vesuvio Q.1000mt
Vesuvius – Pompeii opening times: every day at 9:00, 9:50, 10:40, 11:30, 12:20, 13:10, 14:00, 14:50, 16:40, 17:40
Vesuvio-Pompeii stops: Vesuvio Q.1000mt, Observatory, Entrance. Torre del Greco motorway, Pompeii motorway exit, Via Plinio, Piazza Anfiteatro.

When you arrive at the crater (about 40 minutes of bus) you can
purchase the ticket for the entrance.

Assuming it's the Grand Cono you want to see:
I wouldn't count on buying tickets "at the crater". The park's website states that tickets are only sold online, are timed entry (they do sell out) and " internet connection close to the entrance is extremely weak or intermittent so visitors are advised to buy tickets before arriving at the open area..."

According to a browse through reviews on TA, that appears to be the case. People trying to purchase online AT the entrance have had a devil of a time.
https://www.tripadvisor.com/Attraction_Review-g1602959-d195494-Reviews-Vesuvius_National_Park-Ottaviano_Province_of_Naples_Campania.html

Sooooo, this is the official ticket vendor for purchasing in advance:
https://vesuviopark.vivaticket.it/en?qubsq=fc3c410c-b832-4908-a406-722f652b7a00&qubsp=5ab9f2a9-9c9e-427f-b974-d49ad4936d9d&qubsts=1703635070&qubsc=bestunion&qubse=vivaticketserver&qubsrt=Safetynet&qubsh=a349fc1bb10bba27029042ae4c211093

Other info:
https://www.parconazionaledelvesuvio.it/en/visit-the-park/the-paths/the-great-cono-2/

I believe they're using the word "GUIDATA" loosely: it doesn't mean a tour led by a physical guide but self-guided walk to the crater. Happy to be corrected if I'm wrong.

Thank you all for responding! This is very helpful information!