If I already do the redirect, do I still need to set a preferred domain?

I did, and I think it can only help (it certainly can't hurt to). The main scenario I can see this being of importance is if you recently started redirecting to a single domain and Google has previously crawled your site, setting a preferred domain may help to regain your page ranking.

I did both. When I was digging through the google webmaster help docs, it said that they recommend doing both (setting preferred and 301 redirecting).

Are there any relative merits to standardizing on a www sub-domain versus standardizing on non-www sub-domain?

There was a huge debate on this a few years back, however most of that seems to have died down now. Matt Cutts discussed it a few years ago: http://www.mattcutts.com/blog/seo-advice-url-canonicalizatio...

I think it's a matter of personal preference - just be consistent with whatever you pick.