Really there are little differences between both languages. To get an idea, the same as happen between American and English. Then your choice should be aimed at if you will have more contact with Brazil or Portugal. As well as with the Spanish language has been an agreement on a common grammar for all Spanish-speaking countries, this has not happened, finally, with Brazil and Portugal. Anyway, the differences aren't significant at the end. Thing different is the pronunciation.

Upon asking a Brazilian the same question, I got the answer,that there are really slight insignificant differences between both Portuguese. You seem to be learning Spanish or speaking it , Portuguese has very similar vocabulary. To start with you can take some classes to know how to pronounce and to learn the simple basic vocabulary and grammar ,that would be enough to depend on yourself using online lessons and finding suitable language partners to practice with later.

There are a few differences and the main one is the accent. For example, simple words as comb: "peixe", sound like "peishi" in Brazil, and "pash" in Portugal. The slangs are also different and they can change depending the area specially in Brazil: is not same listening to a portuguese speaker from Rio, than a speaker from the south or São Paulo. The other main diferences are using "você" (brazil) and "tu" (portugal) for "you" and the conjugation of the verb "falar" (to talk) as eu falo, você fala/ tu falas. Other words can also be spelled different as direcção (Pr)/ direção(Bz) for example. Good luck!