You should do Paestum, NAMM both easy train from Salerno and I would do Pompeii as well but you can also do it from Sorrento if your Salerno schedule gets too crowded.
You should do Herculaneum from Sorrento and can do Pompeii from there as well. You can do Capri from Sorrento or Amalfi you so really do have some options in your schedule if you want to be flexible with weather or days.
Pompeii from Salerno lets you off further from the main entrance but coming in the southern (Arena) entrance also means you will enter with fewer people into less of an anthill situation. If you are going to make a day of the park - and you can spend a whole day - I think you'll see all the same things from either entrance. If you are looking to do a 2 hour visit the main entrance is better.
Salerno has a wide pedestrian shopping street Corso Vittorio Emanuele that runs from the train station to downtown. I reccomend staying anywhere in this area for easy access to strolling and the train station. Once you hit the old town it breaks down into a series of old streets, alleys and passageways. Restaurants and bars are scattered all over in this area. The cathedral - especially the basement - is worth touring and search the oldest parts of old town for murals and art alleys.
If you're in Salerno for an extended period of time do not miss the eté Prime at 174 Corso Vittorio Emanuele tucked away between the clothes shops and bank. The front opening onto Corso Vittorio Emanuele (the wide pedestrian only shopping street) is small hallway but set back from the street is an amazing grocery store worth knowing about. The store is kind of like Conad meets Whole Foods and one in Salerno has high end goods at really good prices. I saw 6 kinds of local specialty Buffalo Mozzarella for 2-6e, selection of bakery breads, and shelves of Barolo starting at 12e and topping out at 23e.
The many fruit and daily needs places that dot the street are fine for everyday things but if you have a kitchen or want to put on a real spread and a nice bottle of wine this store is a great place.
Enjoy sud di Italia,
=Tod