Transportation

If by yourself the train will be easier, cheaper and more convenient.

Train. It's also more relaxing and you get to enjoy the scenery and not worry about getting lost.

mis,

I absolutely agree - take the train as it will be more efficient, quicker and certainly more relaxing. There are a few "caveats" regarding rental cars in Italy, which several people have posted about recently here on the Forum. There are also a few "caveats" when using trains or other public transit in Italy, and if you've never travelled there before you'll need to be familiar with those.

Regarding each of your journeys....

• Rome to Siena - you'll likely have to make at least one change on that route, either at Chiuisi or Firenze SMN. You'll arrive in Siena at the bottom of the hill, so will have to use a Taxi or Bus to get up to the town.
• Siena to Venice - in that case, you'll have to take a Taxi or whatever down the hill to the rail station. There will likely be one train change at Firenze SMN and then high speed Freccia to Venice. An alternative would be to take the Corse Rapide (express) Bus from Piazza Gramsci in the centre of Siena to the Bus station in Florence. The Bus trip is about an hour. It's only a short walk from the Firenze SMN rail station, where you could connect with the train to Venice.

For the few rail journeys you'll be making, I'd probably just buy tickets when in Italy, either from a Kiosk or staffed ticket office.