Yea 13 watt 50/50 should work over that for shrooms, and what not.
If you have decent LR then a
power head would be all that was needed for circulation with the LR doing the filtering. A skimmer would be way overkill on a 3 gal tank.
If you wanted (but not needed) you could put a HOB on it instead of a powerhead. That would allow you an area to put carbon in on a temporary or permanent basis. (I prefer "Purigen" -- a synthetic carbon)
There are a lot of people doing a reef in a 2.5 gallon Minibow tank with a 10 watt PC over top of it.
My 4 year old son for example ---- his crab "Godzilla" just recently went to the great reef in the sky --- tears of sorrow --- he was getting old so it was sort of expected. Anyway we have the tank back home from his classroom at school and are going to put a few frags in it along with a shrimp or something.
Just watch out about over feeding cause it's a small tank that can go bad quick and keep on top of those 1/2 gallon (or less) water changes.