I'd suggest going to Darkroot Forest/Basin and getting all the nice equipment tucked away back there. Also, this will give you a chance to stock up on Purple Moss, which you will most definitely need in Blighttown. After that, go to the Lower Undead Burg, fight the Capra Demon, then use his key to access the sewers. From there, you can access Blightown and Queelag's Domain, which will let you ring the second bell. It's fairly straightforward from there, though I would recommend putting off the Painted World of Ariamis until after you finish Anor Londo. Be sure to also try and enter Blightown from the Valley of the Drakes, there is a Fire Keeper's Soul on the way there that can be easy to miss.
Also, don't be afraid to explore New Londo Ruins before you need to go there. You can't progress all that far, and there is some nice stuff to find (plus the only NPCs who can cure Curses for free). The Ghosts aren't too difficult so long as you remember to use Transient Curses, and don't let them grab you.
You shouldn't need to visit the Catacombs until after Anor Londo, which will take you down into the Tomb of the Giants. You'll want a divine weapon to deal with the skeletons. I recommend Astora's Straight Sword. You can find it sitting under the Undead Dragon in the Valley of the Drakes. You can actually grab the sword without aggroing the Dragon, but there is also a nice shield there you'll have to fight for.
Stats don't matter all that much in Dark Soul's, with the exception of stat requirements on weapons. The only stats I put much into were Vitality and Endurance, nearly all my other souls went into upgrading equipment, which pays off much better in the long run. If you want to grind though, there is no reason not to. Enemies don't scale, so if you think the extra levels will help then go for it.