More Sintra questions and train confusion
 

We will be doing a day trip to Sintra from LIsbon mid May and wanted some advice as to the best way to optimize our time there. I see there has been some discussion of this but I did not see anything that would answer my specific questions except maybe the option of using a Tuc tuc which might be a good idea
We want to cover these three site. We are walkers/hikers but are interested in preserving time for the sites themselves.

Pena Palace and the Pena Park,

the Moorish Castle,

Quinta da Regaleira.

My questions are

Which order should we see them in that would make the most sense? Also which will be more crowded later taking that into consideration or as its heavily touristy ..maybe that does not matter as all will be crowded at all times?

Would it be faster to take the hop on off bus to get from one place to the other.

I was thinking to walk to Quinta da Regaleira. first from the train station as that appears to be a 20 min walk.
According to google maps walking to the Moorish Castle from there would be an hour and 4 mins so maybe a tuc tuc from there if they are available?
and then another 30 mins to walk to Pena Castle and Park which we could do

Or should we do the reverse and start with Pena?

We don't mind walking but the sites themselves appear to require a lot of walking and it will make for a long day.. just trying to fit it all in..

Plan to get there early when the sites open (9:30) and leave late in the day perhaps even have dinner there providing how late the trains run back to Lisbon. I have seen two different train schedules with conflicting info so not sure about that either.

Any advice would be appreciated
Thanks!

My only advice is to take a bus to get from the station to the sites.
Last train from Sintra to Lisbon-Rossio leaves at 23:31. Train schedules HERE