You haven't given us any travel dates, so I arbitrarily chose May 15 for the purpose of my rail-fare research.
For each leg of your trip I'm showing two fares found on the Trenitalia website for tickets purchased today. The low fare is for travel on May 15 (though prices can vary from train to train); the high fare is for travel tomorrow. As you can see, they practically give the tickets away if you buy them several months ahead of time, but you'll usually pay several times more for express-train (Freccia) tickets if you buy at the last minute. Even so, the last-minute ticket prices are not exorbitant in Italy.
Milan to Padua: €10.90 to €47
Padua to Venice: €4.80 every day (a regional train with fixed fare)
Venice to Florence: €18.90 to €59
Florence to Rome: €12.90 to €55
Rome to Naples: €11.90 to €52
Those fares include the seat-reservation fee that's mandatory on all the trips except Padua-Venice.
You can research fares on your actual planned travel dates here:
Trenitalia
Italo (Don't use Italo for Padua-Venice.)
On any given trip, Trenitalia or Italo might be a bit cheaper than the other. Since Italo runs only express trains, you don't want to use it for the short hop from Padua and Venice; you'd be paying for speed but not really getting it.
On the Trenitalia website (but not on the Italo website) you must use Italian station names. These are the ones you need for the itinerary you've laid out:
Milano (Tutte le Stazioni) -- that means "all stations"
Padova
Venezia S. Lucia
Firenze S. M. Novella
Roma (Tutte le Stazioni)
Napoli (Tutte le Stazioni)
Once you have your hotels pinned down, you can consider whether you want to try to find a train departing from or arriving at a particular station. Each express train normally stops only at one station in a city.