I disagree with learning Portuguese and Spanish at the same time unless you have a pressing reason (or person whom you want to talk to) for pushing ahead with Portuguese. There are few languages so closely related. I think you could end up speaking Portuñol. 

I'm upper intermediate and I'm still waiting until I have a full adult vocabulary (both active and passive) in Spanish before adding in Portuguese. The amount of false cognates between Spanish and Portuguese is particularly troublesome. 

With Spanish I'm making sure I have all the false cognates handled between English and Spanish before going near the false cognates between Spanish and Portuguese. 

I've tried learning Portuguese and it's a breeze, but even at this point in the game, I think it's going to be much better when I have a super strong foundation in Spanish to jump off of. C1 level I don't think is far enough long. I'm finishing up with the Spanish first. I think of Portuguese and/or Italian as my reward at the end of the Spanish tunnel. :D

Mike, I recommend you learn boths without any problem, don't worry the Portuguese can be similar with Spanish but Spanish isn't Galician so you don't will have problems, will be a great advantage and will save you time. The accent in Portuguese is different from the Spanish, is more easy someone who learned Portuguese learn after Spanish than who learned Spanish and after Portuguese, but if you have a good level you don't will mix, because you will learn they have differences :) They are half-sisters languages not sisters :p the sister of Portuguese is the Galician

I recommend simultaneously because the basic grammar structure is almost identical, if you wait later, then the slight grammatical diffferences will be a bit tedious, and you will be more likely to always mix Spanish with Portuguese.

Both languages are very similar and the writing is easily understandable. They are also, to some extent, interchangeable. I learnt Spanish first then Portuguese, and I find it very easy to improve Portuguese. I realize that I have known so many Portuguese words due to its similarity with Spanish. I am not sure about learning Portuguese first then Spanish. I think any way is fine. 

I recommend simultane too!