On my stock exhaust, I polished the "face" of the muffler and put on a chrome tip. Then I painted the rest flat black. I think it looks much better than stock, and much better than fully polished (I was going to fully polish it). I would say keep the tips polished, then either paint the whole muffler, or everything but the front. You can always try keeping the front polished and if you decide to do the whole thing, it is easy to just use more paint, rather than stripping the old.
It is hard to keep the paint nice though. Mine is pretty chipped up but it gets dirty too so it covers it. I have had it like this for 3 years and I will say that it is unlikely the paint will hold up for any long period of time, even very durable paint. But, if you have to paint once every 3 years, not that big of a deal.