you said the sprockets showed "slight, a little" wear.
your best option is to replace the chain now (I prefer a ring chain but that's a whole different debate).
otherwise, your sprockets are going to go south fast because your chain is worn. A new chain will never know the difference that it is riding on "slightly worn" sprockets.
chain adjustment is key, make sure you follow the manual and do it right.
if you follow my advice and get a ring chain, even with infrequent lubing you will be good to go for at least a season, all you'll have to do is keep an eye on the chain slack but typically it's stays very stable with a ring chain because the chain doesn't wear much.
the "replace it all at once" theory sounds logical and the folks selling the parts probably started it, but from a practical sense on several bikes i've put a new oring chain with sprockets worn half way through the teeth, the sprocket wear nearly stopped and the system was good for at least a season after that (and that's back when I rode a lot).
I love these debates (uh oh, here comes Jay bird)