Who can choose a solution?

I find it fairly useful to have a post tagged as the solution if the original topic is a question. I don’t think people are used to doing it themselves. Is it appropriate for me to select a response as the solution even if I didn’t ask the question?

Sure. The original poster should mark the solution once their problem is resolved, but moderators are welcome to do that too if it’s clear that the case is resolved. (All T/CAMs have moderator status at this point).