"Learn swimming" is the normal thing to say. It implies a systematic attempt to learn something completely. "To pick up" implies learning that is quick, casual, perhaps incomplete. "I'm taking two lessons a week so that I can learn Spanish." "I've never studied Spanish, but I was able to pick up a little Spanish when I was in Mexico City for a month on business."

Sorry - yes. Paul is correct. That is more natural. I focussed on the two options, and missed that.

Would you guys really say 'learn swimming?' To me that seems a very unnatural thing to say. I would always use a form of 'learn to swim', not 'learn swimming.' E.g I am learning to swim. I learned to swim when I was five years old. My friend is learning how to swim etc.

Learn swimming. 'Pick up' is when you gradually learn something by hearing or doing little bits occasionally over time. So you can pick up a few words of a foreign language, or pick up building skills by watching and helping someone. But you wouldn't use it for something that you were actively trying to learn, or going to lessons for.