Start small indeed. I hear what you're saying, there are just so many causes out there!
I've gotten to know my local councillors very well, by going to their surgeries, safer neighbourhoods meetings, making sure I strike up a conversation if I bump into them, things like that. Not protest exactly, but I do feel like they might at least listen to what I have to say if there is a burning (local) issue. I have a few little examples, like the makeup and positioning of our local recycling depot, planning applications, little things like that. Getting involved in the democratic process.