I agree with LittleHoov. The water pump isn't expensive and it's better to shoot for those areas first. Me and my brother changed it in a matter of an hour. Mainly due to the tight fit of the engine. And trust me, I'm no mechanic, but with an extra set of eyes, we were able to nip it in the bud.
The gunk/sluggish material in my radiator was noticed on the radiator cap the most. I got some of it out after flushing it, but after I changed it out, we found a lot was still left in it.