As an English native speaker you might have a hard time finding Norwegian people to practice with unless you can offer another language to do the exchange. Even though we use our local dialect while speaking to each other I am sure you could find someone willing to speak to you as if (s)he was reading from a book.

I think the choice really depends on what you want to use the language for, if it is to communicate with as many native speakers as possible then you should probably choose Swedish but if you already have Norwegian friends or you want to use it for work then Norwegian would be your best choice. Norwegian also has the added benefit of having Danes understand you a lot better than if you were speaking in Swedish, although you will probably struggle trying to understand them either way.

How interesting that you would like to learn to speak one of these Scandinavian languages. I've noticed, in a few different contexts, Norwegian having been argued to be one of the easiest foreign languages to learn for native speakers of English. (I don't know if that is something that would affect your decision, though.)

It is true that when speaking to Norwegians from different parts of the country (as well as when watching television/listening to the radio etc.), you will come across a wide variety of dialects. Although there are a lot of different dialects in Sweden, too, I believe there is more of a tendency there to moderate the way one speaks when in formal settings or when on television/radio etc., whereas local dialects are being used when in informal settings, like when spending time with friends and family.

That being said, it would probably be most useful to select the language you believe to be the most relevant to your life: Do you have more friends or potential friends from Norway or from Sweden? Are you planning to travel to one of the two countries? Or perhaps even wanting to study/work in one of them in the future? Which of the two languages simply appeals to you the most?

Whichever one you choose, both Swedish and Norwegian friends will be able to help you out using English explanations whenever required.

And if you were to tell your Norwegian friends that you are a beginner, they would very easily be able to adjust their speaking to sound as close to the written bokmål as possible.

Elise: Most Norwegians can Bokmål? I could, if bokmål was a verb.

Marie: Nynorsk is based on a combination of western dialects and it is a complete waste of time to even bother with. No one speaks "nynorsk" except news anchors who are faking it.

James: "It's all the same language" - That's a matter of perspective but you are not entirely wrong.

Edit: Self-moderated...