A taxi would obviously be easier. Depending on where your hotel is located, you could take the series of escalators from the train station up to the town.
But why not take the bus, which drops you off right in the town centre?
Which hotel? A taxi dropping you off at either taxi station would be around 10 Euro, it will be few Euro more if it drops you at your hotel.
Butting in because this is relevant to our situation. You say "either taxi station" - I take it this means there are only two, where are they located? I'm thinking that since we must leave our restaurant by 20:30, and the next (and last) train to Florence isn't until 21:40, we could wander for a bit after dinner to see something of Siena at night, then head to the the taxi stand to cab back to the station
We were just in Siena and had planned to take a bus from the train station to our hotel, the Hotel Porta Romano. First of all it is many sets of stairs and 3 or maybe 4 escalators from the train station and through, yes through, the shopping center up to the level of the bus stops. I had researched the buses quite a lot, but after that long haul with suitcases, the bus stops were confusing. We ended up hailing a cab to our hotel. There were lots of taxis at the train station and I would recommend taking one right off. The train station is pretty inconvenient to the old town to walk to.
The following day we rented a car from Budget and that was an experience. I had booked an Automatic transmission car and had 2 confirmations from Budget, the most recent one 2 days before we arrived. Took a taxi to the rental counter and was nicely informed that "We don't ever have any automatic cars here - they only have them in Florence!" I haven' t driven a stick in 40 years and didn't want to practice on the narrow streets of Siena and the curvy narrow roads of Tuscany, so my sister said she could drive.
My advice is to rent the smallest car you can fit into! Parking spots are tiny and you won't want anything even as big as a Ford Focus. The Fiat 500 was perfect & glad we switched. Google maps worked great but it does use data.