You don't need a rail pass for Rome. Buy train tickets on Trenitalia. You can get discounts with advance purchase as cheap as 9€ for the fast AV train which is cheaper than the mandatory seat fee you would have to pay in addition to a pass. Register on Trenitalia before purchasing.

http://www.lefrecce.it/B2CWeb/customerLogin.do?parameter=registerCustomer

2nd class on AV train:

http://vocearancio.ingdirect.it/wp-content/uploads/2009/12/user_39_tav_frecciarossa_interno.jpg

Discount info:

http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=492299e8e609a110VgnVCM1000003f16f90aRCRD

I would think super economy tickets would be cheaper than the family discount, but you could check that also.

http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=91fb335a9a605210VgnVCM1000003f16f90aRCRD

The pass would only cover the train to Naples. From Naples you take the local commuter train Circumvesuviana to Pompeii Scavi.

http://www.vesuviana.it/web/en

Do also check out the other operator of fast trains on the Rome / Naples route - the Italotreno company.... who offer 10 per day each way, with a simple timetable that's available here:

http://www.italotreno.it/SiteCollectionDocuments/Orario-Treni-Italotreno.pdf

... and English webpages here:
http://www.italotreno.it/EN/Pages/default.aspx

They also offer reductions for advance purchases, with prices from €20 - and have, as I recollect, an earlier fast service at weekends (or maybe just Saturdays) than Trenitalia.

However, whilst running to the same place (Napoli Centrale), in Rome their trains operate out of the recently renovated Tiburtina station, a couple of kilometres east of Termini - which may or may not be more convenient for where you're staying?

With either, you'll probably find this useful:

http://www.fodors.com/community/europe/through-naples-to-sorrento-or-pompei.cfm

(Look to the end of it for recent updates!)

Peter