1. New Londo/ Four Kings
2. Lost Izalith/Bed of Chaos
3. Tomb of the Giants/ Nito
4. Duke's Archives/ Seath
I feel like it's the most logical order. Four kings first because they're easiest in my opinion, (plus Darkwraiths), Izalith to get the sunlight maggot, TotG because it's much harder and sunlight maggot helps out a ton, and last Duke's Archives because it's hardest in my opinion.