Cheapest place to fly into?

Only someone who knows your origin airport and travel dates can provide a useful answer to this question. From my origin, Munich is often a rather cheap gateway, and Madrid isn't bad. In my experience, you do not know what will happen with open-jaw (multi-city) tickets until you plug your airports into Google Flights, kayak, etc. Try it and see. Just price out the two transatlantic legs. If you need a mid-trip flight, price it out separately. For that, I use skyscanner.com.

Ah, of course. Leaving from Portland, OR, May 20, 2019, returning...not exactly sure, mid June. We're pretty flexible on arrival and departure locations.

Actually, it might be the weather that drives your decision. By June Madrid can be quite hot, so making that your first stop in May and then gradually working your way north might be the better option if only to avoid the worst of the summer (or late spring at any rate) heat at your various stops.

Icelandair flies out of Portland, but you'd have to stop in Reykjavik and catch a connecting flight. Delta flies to Amsterdam, however I suspect their flights are very expensive.
If you're willing to drive the 160 miles to SEATAC, there are a couple of budget airlines flying into there.
Norwegian Air Shuttle has seasonal service into London--Gatwick. You can take EasyJet from Gatwick to virtually anywhere you want to go in Europe really cheap.
Aer Lingus also has service into Dublin and connecting flights to many European cities. Ryanair also has a large network flying to most popular European cities from Dublin.

You are in luck living in Portland, as the low-cost carrier Condor flies out of there. We flew them home from Europe last month and it was fine. And our kids and grandkids flew over on Condor from Portland. Just be sure to understand what you are and are not getting. And read reviews. Some are not happy with the food, but our kids had no complaints.

One nice thing is they price their flights one way at a time, not round trip, so you can book one way at a time.

For Madrid, you would fly to Frankfurt and change to a Lufthansa flight to Spain.

To return from Munich, price the difference between starting from Munich with a flight to Frankfurt for the overseas leg, versus taking the train to Frankfurt for the flight.

Or maybe they have direct flights to Munich next summer.

I took a very quick look, and it appears that the Madrid/Munich combo yields a fare that is substantially higher than round-trips to either place if you stick to legacy carriers. I see, though, that Frankfurt RTs are much, much cheaper than Munich RTs, so I'd throw Frankfurt into the mix. Unfortunately, even using Frankfurt as your departure point, the only markedly lower multi-city fare I found had two stops in each direction. It was under $1000 vs. around $1400 or more for the faster options.

Sometimes, despite the conventional wisdom, the multi-city fares are just plain too high. I'd explore the budget-carrier options previously mentioned.

I see some non-stop or one-stop options NYC-Madrid/Munich-NYC for $600-$800. I have never tried to piece together separately-ticketed domestic and international flights, but to save $660-$800 per ticket, I'd consider spending the night near JFK (especially if there was someone splitting the cost of the hotel room with me). But even with a night in NYC, any separately-ticketed itinerary retains a bit of risk.

Condor will,get you home from Frankfurt on a direct flight to Portland for as low as $399 for some dates in June. There are lots more choices in the $420-450 range.

Going TO Spain, Condor is not all that cheap; May 20 and other dates in May are $800.

But if you are willing to fly from LAX, Norwegian Air will take you to Barcelona for $347 on 20 May. (They do not fly into Madrid). That is their lowest Economy fare, so make sure you understand what you are and are not getting (like meals).

So that comes to $650'for the two flights if you can do without any frills on Norwegian. Or pay $90 more for Economy +.

Condor's Economy includes checked bag, seat selection, and two meals.

PDX (Portland) - OAK (Oakland) Southwest Airlines
OAK - BAR (Barcelona) Norwegian Air Shuttle - non-stops Mon/Thu/Sat currently from $180 one way (one-stop flights 7 days/week)

That is even better than the LAX flight I suggested. Hopefully the price is comparable. Are the flights from Oaklland daily? They are from LAX. Just something to consider.

Three weeks for 2 countries wouldn’t give you much scope beyond the big cities.

ARRIVE Munich (4N)
Train to Berlin (4N)
Fly to Barcelona (4N)
Fly to Granada (2N)
Train to Seville (3N)
Train via Cordoba to Madrid (4N)
DEPART Madrid

Aside from Condor and Iceland Air, you may actually have ok luck with Delta depending on your dates, as they have direct flights from PDX to Amsterdam and London Heathrow during the summer - you can catch easy flights to Spain and Germany from there. Set up a Google flight tracker to see how prices change. If you're set on leaving May 20 (a Monday) prices may be higher just because it's a weekday.