Paris to Murren, Murren to Florence - How?!?

When you get to Basel you could buy a Swiss Half-Fare card for $122. These are cost effective as long as you expect to buy $244 worth of point-to-point rail tickets in Switzerland. You could also buy a 3-day, second class Swiss Travel pass for $220. Which option is most economical depends on your exact travel itinerary; you'd need to price them both to know.

Personally, I recommend the Swiss Travel Pass. It's valid nearly everywhere (not high mountain stuff like the Jungfraujoch), covers rail, boats, cable cars, buses, and nearly all museums. The HFC covers all that stuff, too (except museums), but you still have to buy your ticket each time, whereas the STP is your ticket. It's a nice convenience. I think you have to buy the STP before you go.

It is really better to speak in Swiss Francs (CHF) rather than dollars (USD), as when in Switzerland, that is what currency all prices are posted and quoted in. Of course, right now they are virtually the same. Note that the Swiss Travel Pass only gives a 25% discount on the Wengneralpbahn above Wengen and Grindelwald, and the Jungfraujochbahn. It is valid on the Schilthornbahn cable car from Stechelberg in the valley floor to Muerren, and a 50% discount above that. The Half Fare Card, 120 CHF, gives a full 50% discount for all of these.

Paris->Basel purchased from www.sbb.ch/en and print at home.

Basel->Murren purchase in Basel OR if you have a STP you just jump on any train you want without buying additional tickets. If you have a Half Fare Card then you'll need to buy tix Basel->Murren.

Murren->Firenze SMN can be purchased from either www.sbb.ch/en OR you can buy the Milano Centrale -> Firenze SMN portion at www.trenitalia.com and you can get some super cheap prices on that portion if you book as soon as the tickets become available.