Ways to get to Pena Palace from from Sintra Station

We walked so didn’t have experience with other modes of transport. I think it’s possible to do all three things you listed. I would suggest starting off early in the day. Buy your ticket to Pena Palace online choosing the earliest timed entry that works for you. Given train transport from Lisbon and our morning routines, we choose the 10:00 entry. The earliest timed entry we saw was 9:30. We arrived at Sintra before 8:30 and just started walking to the palace.

Taking the Scotturb bus (I forget the bus number) is a popular choice but according to this YouTuber, they are scammers. Check out his video from 6:05 onwards, but you might want to watch the whole video. His name is Tony Galvez and he speaks Portuguese and Spanish: https://youtu.be/ao-T6ap8HvU

Here’s another video showing the bus option:

https://www.youtube.com/watch?v=6D3-a1q9O50&t=2s

Another option is to take a day tour that includes sintra:

https://lisbonriders.com/group-tours/sintra-cascais/

I will be in Lisbon in march and will probably take the buses from the sintra train station.

In September, we took a Bolt from the front door of our Lisbon condo right to the entrance of the Pena Palace, €35 for six people. A smaller Bolt for up to four people is estimated to be about €27 (see google map on android phone for latest estimate). This was a great way to avoid the crowds on the train, the bus and at the entrance or at the castle, which can become quite massive as the day wears on. If you have four to six people to share the Bolt fare, it should be much cheaper than taking the train and the bus.

Walking from Pena Palace to the Moorish Castle is not too difficult.

After we visited the Moorish Castle, we opted to to take a Bolt straight back to the Lisbon condo. It only cost €28 for the six of us. The route down is shorter.

If we wanted to take the bus down to the Sintra city center, there was a long lineup and wait for the 434 bus and they were asking €10 per person. That is the all day cost which apparently is non-negotiable
because of the monopoly by the bus.

Alternatively, there were local drivers (not Uber or Bolt) hanging around the Pena and Moorish entrances offering to drive people down off the mountain to the city center for €5 per person.

A Bolt down to Sintra would probably be very cheap, but I heard that bolt drivers will not accept such a short fare, because they have to drive a long way up to pick you up for a very small amount of money.

I took a tuktuk. The bus was jammed packed with people. It was under 10 EUR if you shared with other people. I only visited the Pena Palace and the Regalaira, but I think you can do all three if you start early.

If we wanted to take the bus down to the Sintra city center, there was a long lineup and wait for the 434 bus and they were asking €10 per person. That is the all day cost which apparently is non-negotiable
because of the monopoly by the bus.

This might be a reason why Tony Galvez (the YouTuber whose link I posted above) said Scotturb bus transportation is a scam.

And indeed, the wait for the bus can be long and those buses can be overflowing.

We decided not to worry about ground transportation by walking everywhere. Once we got into Sintra by rail, we just started walking. We walked to Pena Palace with a nice safety margin to wait for our 10:00am timed entry (I'm still surprised that 9:30am was the first entry available; doesn't seem early enough to me). Then we walked to Moorish Castle. Then we walked to the centre of historic Sintra and while we were going to go to other sites, we decided to meander around town instead. I did learn that I would love to stay overnight in Sintra so that I can have an extra day there, although I haven't investigated to see the cost of hotel to see if that is within reason with our budget.

If you don't find Lisbon's hills challenging at all (we didn't and we walked everywhere in Lisbon), I think you'll find the walk in Sintra really quite pleasant and it's amazing to trod the ground there and just observe and absorb the scenery. It's not to say we weren't tired at the end of the day. We were, but after a good night's sleep we were up and ready with no physical fatigue :)