For target shooting or just plinking, it really doesn't matter. Use what ever you prefer and/or is cheapest. Different loads will shoot to different points of impact but that is negated in the 686 by the adjustable sights. Myself, as a reloader, a rarely vary from a hardcast 158 grain semiwadcutter (SWC) or a 148 grain wadcutter (WC).
Just be sure to thoroughly clean the cylinder chambers once you are done firing 38 special. They are a bit shorter than 357 and you can get a carbon buildup in the chambers that if not cleaned, can make it difficult to load and extract the 357 rounds.
If you are looking for a light factory load, check in to the 38 special cowboy loads offered by several manufacturers.