I would start with what points/miles do you have to work with and then go from there. Flying to Barcelona, my first thought would be Iberia even though you'd likely have a connection in Madrid. I had Avios miles sitting in BA collecting dust and transferred those to Iberia to book our 2 J seats to Barcelona from Miami for our VV med cruise in a couple of months.
I think you need to have an Iberia account open for 3 months first. But you can transfer to a newly opened Iberia account from Chase or Amex. Chase transfers are instant and our travel companions opened up new Iberia accounts and transferred their points right away to book. TPG (yeah, yeah, I know) article showing the drastic difference of tax savings booking with Iberia over BA
https://thepointsguy.com/guide/move-british-airways-avios-to-iberia-lower-fees/
I also agree with a previous poster about working your way backwards. That is also good advice.
BTW I'm pretty sure AA has some direct flights to BCN out of MIA, CLT, JFK and ORD
Hope this helps