It's an amazing place. You can stay in loads of places in Naples depending on your budget. Sorrento round the peninsula is nice, again loads of different hotels depending on your budget. Probably better than Naples because it's a nice seaside place. Naples is definitely a bit dodgy if you end up in the wrong bits.
Get the train, cheap and efficient, there are 2 stations, one for the excavations "pompeii Scavia" and one for the modern town where you DO NOT WANT TO GO. If you go from Sorrento it's a really interesting journey through the mountains. The entry fee is cheap, use the loo at the entrance as it's the only one I remember being there. I'm a complete coward but felt totally safe travelling with the family to the site so you should be OK
pompeii is a very very big site and You can get a cheap guide book at the shop at the entrance, but things I liked were:
the "garden of the fugitives" at the back of the excavations. Several bodies including a child hiding under it's mother, very sad even after 2000 years.
The tesselated entrance hall on a Villa " with "Cave Canem" (beware of the dog) on it
The public bath house has a very well preserved body in it. The detail is amazing right down to the wrinkles round his eyes and the buckles on his sandals.
The amphitheater at the back where Christians were eaten by Lions.
The long road with tombs and monumets, can't remember it's name but if you look on the the map it's to the left of the main entrance
The knocking shop, and the penises carved into the pavements guiding the way to it. pompeii was a port frequented by people who couldn't speak latin so this was the quickest way to guide them to it, hence the Frankie Howard thing
The worn cart ruts in the road, makes you realise people did really live there
There is one thing not in the guide books. About half way down the main street if you go off to the right there is a modern wooden staircase that leads up to roof height. This is a viewing platform for several bodies that tried to escape across the roofs, including a woman and her slaves, which is really interesting. To get there there are lots of little gates of the main road that are usually locked, just step over them or ask an attendant if there's one around, a few euros helps. you will have to search for this but it's of the tourist track and well worth a look
I went on a half day tour with a guide one year and then went back on my own for a day which did the place justice, the problem with the guides is that although they tell you a lot they only take you to the main bits which aren't always the most interesting bits
If it really interests you seriously consider going to Herculaneum which is nearby, this is much better preserved as it was buried by mud not crushed by ash and you can actually go into buildings and see the tiling and frescos on the walls, you can do this at pompeii but Herculaneum is better, the public bath is perfect including the glass in the entrance windows and the tiling of dolphins in the hall looks like it went down last week. There is also a Villa that would have been on the waterfront which now looks out at a wall of dried mud but you can see that it would have had a fabulous view
Other interesting things include the National Archeological museum in Naples which has statues and gladiators helmets (titter ye not etc) and Solfatera in the Phlegrean fields which is volcanically active, you can see boiling mud and smell sulfurous smoke coming out of vents in the ground
I went up Vesuvius but thought it was a bit of a disappointment, I wanted lava and smoke but got acres of slag ash and a big hole in the top and someone had their bag snatched at the cafe half way up
Naples has no evacuation plan if Vesuvius goes bang again, it's overdue so you had better hope it doesn't go while your there.