Sometimes I like to "start" in an area, get all the goodies and upgrading them.
For example the catacombs, you can get a scythe and lucerne, get lucky with the crystal lizard and get a green shard. So you'll have the opportunity to get a fire weapon immediately.
Hang around with vamos, kill some (lots) of skelly wheels, maybe get a shield. There's also the black knight, but I tend to ignore those weapons. Terribly OP, those are.
It's also there I found out you get increased souls if you keep killing the same enemy. I almost always skip pinwheel as I think the right of kindling is highly unnecessary.
Then you emerge from the catacombs a true warrior.
This is just an example, it all depends on the focus of the playthrough. I usually do like to go through dragons valley with the key to unlock the lift into the parish, get the fire keeper souls and lautrec for his ring. Sen's skip for the gold serpent ring is also mandatory for me. There's also the lightning spear, steel ring and lost of demon titanite if you need it. I love this game, but the drop rates are complete butt.
Also fun fact, that fake wall in Sen's is the only one in the game that you must hit and can't roll through.