Preparing a deck & playset for re-staining
The answer given to the question you linked to, pretty much covers all you really need to know (IMHO).


  Q. There are few splinters and chipped wood on the deck. How to smooth those out?


Sanding by hand or with a random orbital sander should pretty much take care of those areas. If you need to smooth out "really rough areas", go with something like:


Begin with 60 Girt.
Then move onto 100 Grit.
Then finish with 150 Grit.


Though I'm guessing (not being able to see the actual state of your deck &amp; playset) for most of your sanding needs, 100 &amp; 150 Grits will be sufficient.