what is the best way to get from lucca to siena?

I didn't research any bus connections; I'm usually a train person. Perhaps someone can help with that...

There are nearly hourly trains to Siena, most with a 30m connection in Florence/Firenze. Use Trenitalia.com (click on the British flag in the upper right corner) for schedules. There is no benefit to purchasing this ticket itinerary in advance, so just buy it once you are in Italy. It's 13,30€ for a 3h trip.

It will get brought up that if you take the bus into Siena, you'll end up in the center of town and not 'on the outskirts' at the train station. The train station is hardly on the outskirts of town (it's just not in the main square), and the taxi ride is approx. 10€ or so. Lots of taxis waiting for your train to arrive...

Train (Trenitalia) or bus (Lazzi) to Florence. Then from Florence you can take the Sita bus (75 min.) or the trenitalia train (90 min).

The fastest and least expensive route from Lucca to Siena is the train via Pisa and Empoli. Trip takes about 2.5 hours and costs just over €11. From the Siena train station, you can also take a bus up to the town center (follow directions to station in Rick’s guidebook). Buses going to Piazza Gramsci or Viale Tozzi get you to the same place. The train or train/bus options via Florence take a little longer and cost a bit more, but involve 1 or 2 fewer changes.