You have a couple of options. If you take the Silver Star or Meteor down to Sebring or Okeechobee, one or the other is probably the closest actual rail station to Naples. That option would probably be best if you have someone in Naples who could drive out to one of those two places to pick you up. If not, Amtrak has a Thruway Bus from Tampa, I think, that goes as far as Ft. Myers. And you could always go as far as Tampa (or Orlando) and rent a car there if you wanted to have your own transportation when you got to Naples. Ft. Myers would be about 30 miles from Naples. My wife and I travel down there by car from Orlando (three and a half hours, more or less, by car) two or three times each year, as she has family down there, and once, using the Florida Resident Annual Railpass, which includes that Thruway Bus, she took that bus back from Ft. Myers to Orlando. The station in Okeechobee is unmanned, I believe, so no baggage handling service there. I believe Sebring is manned. Orlando certainly is and although I haven't been to the Tampa station, I expect it would be also. Amtrak could certainly tell you those things one way or the other. Note: the Star, Meteor, and Palmetto have route and schedule changes starting next month, so check VERY carefully on what will be valid for your actual proposed travel dates. Palmetto, for example, will become Savannah-New York and will not travel to Florida at all.
Have Fun!! Naples is lot bigger than it used to be, but still has beautiful beaches.