The key to any finishing or refinishing job is proper preparation.
1) Clean the deck, railings etc well, removing as much dirt, grime etc with a power washer on medium setting
2) Wet the area with a mixture of 2/3 gal water, 1/3 gal bleach, and 1/2 cup TSP.
3) Let the mixture set for 5 minutes, then scrub it in with a stiff bristle push broom wetted in the same cleaning solution.
4) BEFORE the cleaning solution dries, rinse it off with a hose or your power washer.
5) Repeat this in any areas that still look bad or stained with BBQ leftovers etc. This should brighten the wood considerably.
6) Repair any loose boards, nails, screws etc.
7) Let the wood dry completely, usually a couple of days under good conditions before staining.
8) I like to apply stain with a roller on a pole or 1 gal pump sprayer, then immediately over brush with a good china bristle brush to even it out. Don't be surprised if it takes two coats to look good again.
9) Don't wait 10 years again to freshen up your deck!!!!! Good Luck
Best Answer
The answer given to the question you linked to, pretty much covers all you really need to know (IMHO).
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:
Though I'm guessing (not being able to see the actual state of your deck & playset) for most of your sanding needs, 100 & 150 Grits will be sufficient.