Madrid-Portugal 2,5 weeks

If you are starting in Denver, look for a good open jaw flight into Madrid out of Lisbon or vice versa. (Not two one-ways - try booking it as one "multi-city" ticket when you check prices.) Whether that is cheaper than flying RT to/from Madrid depends on when you fly and how competitive the market is flying between Denver and those cities - might be different for me where I live.

You can book a separate flight between Madrid and Lisbon for almost nothing - there are lots of daily direct flights and it is very competitive. I flew Iberia between Madrid and Lisbon and then between Porto and Madrid last month. (One of those was part of my open jaw ticket, the other wasn't, booked separately.) This was my first experience with Iberia and, I hope, my last. There are plenty of other options like TAP, easyJet, RyanAir, etc.

I was in Portugal last month (not Spain other than Madrid airport). You'd have plenty of choices for places to see in Portugal other than Lisbon. I had a few days there - plenty of day trip options, and you can even stay overnight in a town like Sintra (a common day trip from Lisbon) instead. It's not a "seaside town" but it is very touristy, looks peaceful at night. I took the train from Lisbon north to Coimbra (old university town) and then to Porto for a few days. On the way north I detoured off the train a few hours to the lovely little town of Tomar (not touristy at all - but now that Rick Steves says he will add Tomar to his book, that will probably change soon). Lisbon and Porto were both very touristy (not a complete surprise). Coimbra not at all, but there isn't much to see there. A night there would probably be enough for most people, depending on travel style.

Flying between Madrid and Portugal is, by far, the best option. And likely the cheapest. And, I agree with the other poster, try for an open jaw flight to save time and money.
Regarding another smaller town in Portugal - you have a number of options. You might want to research the following towns - Coimbra, Evora, Tomar. Coimbra and Evora have the best transportation from Lisbon. I would not suggest Sintra since it’s so overrun by tourists. It’s likely fine at night but NOT during the day!

As you're learning, connections between Spain and Portugal are surprisingly skimpy. There are some buses, there are a very few trains (often at odd hours, although the Madrid to Lisbon train is a sleeper), and there are flights.

If you do want to combine Madrid and Portugal in one trip, do fly into one country and out of the other, so you don't have to backtrack. Then fly between them. Or, consider seeing just one country or the other on this trip, since it does make the logistics much easier.

I researched a one way trip by rail or bus (or also a tour) from Madrid to Lisbon.

In the 1980s, we took the train from Madrid to Lisbon. I think there is still a train, but I read a couple of years ago that the route might be cancelled.

There were private busses that made the trip, but I was unsure as to how nice they would be. Ultimately, I abandoned going to Madrid (had been there before) and we just did Portugal.

I would only drive between Madrid and Lisbon if you planned to do it over two or, better, three days with overnight(s) along the way. You have the time perhaps?

There are various routes and places to stop, though the obvious one would be Cáceres (one of Spain's most beautiful towns, some say). The rural country is also worth seeing on both sides of the border.

However, I'm not sure what you do with your hire car when you reach Lisbon unless you are making a return trip, otherwise the single journey may be expensive with drop off fees. You could consider Madrid - route with overnight stop before Portugal and then few days in town like Coimbra - Lisbon - back to Madrid via a more southerly route with overnight stop? There are a few paradores available in Extremadura for your stops.

I would only use the train if you are going by Trenhotel, and going grand clase, which is not a cheap option. It is much more civilised than flying and you travel whilst asleep. But some don't enjoy sleepers and it is more functional than "classy" like the Orient Express in the films. I like sleepers, but do it for enjoying the journey rather than the practical getting from to A to B for which flying would be better for Madrid-Lisbon.

Thank you for all the suggestions. Seems like the 2 best options would be the US-Madrid & Lisbon-US airfare, + flying Madrid to Lisbon or at the end of the Madrid visit, renting a car and driving to more remote areas, finishing in Lisbon, but then the last day would be driving back to Madrid. Or maybe just visiting Portugal. Making the drive from Madrid to Portugal, and having the flexibility to include remote areas in the itinerary is appealing, even with the added $ for a car and spending the last day driving back. And thanks for recommending the areas in Portugal to visit. A laid back place with great food/wine would be good.