Yes, you should clean stylii, as well as the records.
Dry cleaning brushes: Any quality artist brush, natural fiber(read: sable). Mine is a .5" flat tip Grumbacher 6661. Used for general dusting, especially since the Clearaudio V. Wood loves to attract all manner of fuzzy crap on the bottom front.
For stylus cleaning brushes, I have the one that came with LAST. Also have a old Discwasher brush. Both these are high-density fiber count with a "flat-top" cut. Both are used with any manner of liquid cleaners on an infrequent basis. Dry use before each play. Wet use w/ Audio-Technica SK301 or LAST on an infrequent basis. As for RRL #9 or DD stylus cleaner? I haven't much doubt they're good, but @ $25/.5 oz? Then again, you don't use much of it.
The Mr Clean is currently costing $3.39 in my area. There is now a competitor, 3M Scotch Brite eraser pad at $1.99.
My first choice is the Signet SK305 electronic cleaner-
www.newolde.com/stylus_cleaner.htm/
Sadly, long gone, once again thanks to Audio-Technica