I think Max may be right about the Iberia price quote bring for BA’s Economy Basic”. You would need to work through the booking page to find out.
Here is the difference, as explained by British Airways for long-haul flights:
https://www.britishairways.com/en-us/information/travel-classes/economy/our-long-haul-fares
Basically, in Economy Basic you have carryon only, no checked baggage. And you are “allocated” a seat, which could be a middle seat on a crowded plane. But you CAN still pay to choose your own seat.
Regular Economy (World Traveller) offers a free checked bag, and you can choose your own seat for free—-at online check-in. If you want to choose your seat ahead of time, and not get stuck with what if left at on-line check-in ( 24 hours ahead of your flight), you will have to pay for the privilege, same as you would in Economy Basic.
So, if you are happy with carry-on only,, and you want to choose your seat in advance, you could book the Economy Basic. You could go to the British Airways website and compare the price offered for that class to the Iberia quoted price.
We fly British Airways every trip (15 and counting) and have booked both through BA and with Alaska miles. No matter who you book with, if you want to choose your seat in advance you will have to pay for the privilege (unless you have high status with BA). Even in business class. We always do.
When booking with Alaska miles they give you both the Alaska PNR code and the BA booking code right on the confirmation; you do not have to call and ask for it. I always take that and go register my flight on the BA website under my BA Executive Club account. Then I choose our seats.
It looks like the PDX BA flights use a 777. You can see the seat maps for these on the BA website:
https://www.britishairways.com/en-us/information/seating/seat-maps/world-traveller-seatmap
If I were traveling solo, or as a couple, in World Traveler, I would choose one of the seat pairs in the last few rows, where the fuselage narrows. That way I could have a window seat with only one other person in the row. But if you are wanting an aisle seat then something further forward might be better.
Unfortunately the seat map does not indicate where those pesky under-seat boxes are located. And I don’t know if all planes have those.