While not the greatest pic, I don't think the anemone you found is an anemone. To me, it looks much more like a tiny piece of clove polyps, Xenia, or Anthelia. Not sure what kind of lighting you have since you're not intending to make it a reef tank, but if you put those up closer to the light, they may survive and grow for you.
I would advise getting rid of the glass thermometer. Depeding on what you ultimately stock it with, there could be plenty of critters that have the potential to break it.
The tank is looking pretty good! What else do you plan to put in it?