Yes, resolution does matter for template picking, but not in the way you think - to avoid as much bias as possible and “Einstein from noise”, you actually want to deliberately limit resolution, which is why templates and micrographs are low pass filtered (by default to 20A). See this thread for a couple of posts with some explanation of why high resolution picking is so dangerous.
Not sure whether your sample is supposed to be a monomer or dimer but it looks like both are present (or there are some “twins” in the same detergent belt, different scientific relevance, same overall effect) but I’d probably take classes 10 and 11 (top right and bottom left respectively) and template pick using just those. You’ll find that due to the low pass filter, it’s not very “specific” and will still likely pick all of the smaller densities, but if not try picking with classes 1, 2 and/or 12 as well.