A couple general tips:
Don't level Resistance. It's pretty useless.
You'll run up on the bridge dragon before too long. (You'll know it when you see it.) While the best way past is to go under the bridge, it's worth making a suicide run to grab the items on the top of the bridge. The Claymore is extremely versatile, and a +15 Claymore is one of the best weapons in the game.
I would recommend checking the Dark Souls wikis. You will miss stuff if you don't. However, there are massive spoilers, so go through each area blind and then check the wiki to see what you missed.
Minor spoilers: If you're in Human form, you can summon NPCs to help you in some boss fights. I won't say which those are, except that there's one in Darkroot Garden, in the area with the stone giants. If you summon that NPC, you can summon her for another, very tough boss fight later in the game?but if you don't summon her the first time, she won't help you with the second.
If you're in Human form and you haven't killed the area boss yet, there are special events that occur in Blighttown, the Depths, Demon Ruins, Lost Izalith, Tomb of the Giants, the Painted World, and Oolacile Township (if you have the DLC) that can give you neat items.
You can grab some neat gear following the advice in the video below, but it's not necessary and you may not want the spoilers.