Barcelona/Madrid/Porto/Lisbon 13 full days in October

You've set yourself a challenge. The number of days you have (really 12 full days--don't count your arrival day) is much more suitable for a visit only to (part of) Spain or only to Portugal. Transportation between the two countries is not very convenient (no fast trains between the capitals, for example), so you're going to have to fly. That'll cost you the better part of a day as you travel to and from airports, allow extra time for security, etc. So your first day in Portugal will only be a very few hours.

Four nights in Barcelona when it's your first stop is going to be an issue, I think. That first day you'll probably be too zombified to do more than walk around, trying to stay awake. With luck you'll be able to enjoy strolling the Barri Gotic, maybe pop into the cathedral (I am not referring to La Sagrada Familia), grab something to eat at La Boqueria if you're not on local meal times (lunch at 2 PM, dinner at 9 or 10 PM). That leaves 3 days for all the go-inside sights, a large number of which require pre-purchased tickets to avoid really long lines. Scheduling is tricky when you only have 3 days.

Whether you can just manage to get by with 3 nights in Madrid depends on whether you're interested in the art museums and your plans for side-trips. I love art, but to me the #1 sight in Madrid is not actually in Madrid, it's the city of Toledo. That's either a full-day trip or--if you're like me--a place to spend 3 nights. Segovia is also a great day-trip; it doesn't have as many important sights as Toledo (the aqueduct is beyond magnificent), but it can fill a day. In Madrid itself, I think most people place the Palacio Real next to the art museums in importance. I don't usually like palaces, and that one was no exception, but I seem to be in the minority. Obviously, you'd need at least a solid half-day just to walk around the center of Madrid and get a sense of the city. So how many days is that sounding like to you?

I haven't been to Portugal recently, but you've chosen the top two cities, I think

If I had your constraints (flying into Barcelona and out of Lisbon), I'd eliminate Madrid from the itinerary this time around. It can be part of a later trip that includes Andalucia.

Do check right away on skyscanner to see what your options are for flights either Barcelona-Porto or Madrid-Porto. I don't know how many choices you'll have. I think Porto may end up needing an extra night since it may be quite late in the day by the time you get settled in there.

If those are the four places you want to visit then I think your allocation is fine. And they are all nice cities worth seeing

Barcelona-Madrid and Porto-Lisbon are straightforward journeys by railway. But, especially if you are not driving, Madrid-Porto is going to be a pain. I suspect flying will be the optimum means (try Iberia or Ryanair?), or you might want to use the sleeper train to Coimbra or Lisbon and then add a connection once in Portugal (a bit convoluted perhaps).

Personally, I might consider dropping Porto - it is a nice city though and would be a shame to miss - and adding a night to each of Barcelona (to then include a day trip to Girona) and Madrid (to include a day trip to Toledo). Without the extra night, I think I would just stay in Barcelona and not consider a day trip since there is a lot to see in the city. Even with just the three nights in Madrid you could still consider a trip to Toledo (or Segovia), unless you are very interested in art galleries (and a large but dull palace), in which case stay in Madrid.

With a trip already planned to Sintra, I don't think you will need any other day-trips and should stay in the city for the rest of your time. But try to find time to cross the river to the other bank (south?), there is a regular ferry, and see that part of the metropolis/region too for a few hours. I think its called Almada.

Thank you both for your insights and suggestions--much appreciated.
Reading more about Porto, we have decided to shorten our Lisbon stay by one day, and to enjoy the drive from Porto to Lisbon.
We agreed with you both...we plan to focus on the most important museums and take in more of the daily local existence and natural beauty---again, thanks.

"Pls note that while the above is somewhat ambitious scheduling....the various tours and literature we have reviewed seem to support this schedule"

I don't feel the that number of nights you have allotted for each place is overly ambitious (some will obviously disagree, but I think they're fine). The problem is getting between them. While we in the US think of Spain and Portugal as practically one country, the transit links between them are surprisingly skimpy. There are a very few trains (often at odd hours), there are some buses (far fewer than you'd expect, and often involving transfers), and there are flights (more than you might think, to fill in for the lack of other options).

As you've been told, Barcelona to Madrid and Porto to Lisbon each take a few hours by fast trains (book NOW for best fares, particularly on the Barcelona to Madrid leg - see below). Madrid to Porto is another matter. Look at Skyscanner to see flights for your travel date: https://www.skyscanner.net/. If you don't like what you see, then drop Porto. You'll still want to fly from Madrid to Lisbon (again, unless you want an overnight train).

For both this trip and future planning, Rome2Rio is a great site to know about. It purports to show all the ways of connecting two places. You should never take it as the last word, and should always confirm schedules and prices directly with the airline, bus company, etc. But it's great at identifying potential problems, before you get too attached to an itinerary. For instance, here's Madrid to Porto: https://www.rome2rio.com/map/Madrid/Porto

For the Barcelona to Madrid tickets, Renfe operates the trains, but their website can be tricky to use (even Spaniards on this forum have complained!) http://www.renfe.com/EN/viajeros/index.html I found this tutorial from TripAdvisor invaluable: https://www.tripadvisor.com/Travel-g187514-c80518/Madrid:Spain:Buying.Renfe.Tickets.Online.html. And be sure to use Paypal, as Renfe doesn't usually work with US credit cards.

If you can't get Renfe to work, you can use Trainline (apparently no markup over Renfe) https://www.trainline.eu/ or Loco2 (small markup) https://loco2.com/. If you wait until the last minute, tickets can be double to triple the price of an advance fare, and some runs will be sold out.

Skip Sintra. Obidos is great though.

It looks like you can fly from Madrid to Porto on Air Europa, Iberia, Ryanair, and TAP Air Portugal. Check the schedules and prices and see if there's a flight that suits your budget and your schedule.