The logical progression through the game is indeed Sen's Funhouse after Blighttown. If you want to do some other stuff first you could kill the Moonlight Butterfly if you haven't yet (boss in the Darkroot Garden, take a right before the sealed door, there's also a bonfire behind an illusory wall to your left there too). The best way through Sen's is to just run past the snakemen, but they're weak to lighting if you want to stock up on gold pine resin, and there's also a lightning spear in there too.
And not yet, but you can. Buy the Crest of Artorias from Andre the Blacksmith for 20K souls and you'll be able to get into the sealed door, but I would wait until later to actually go do stuff beyond it.