I'm actually in the middle of a 'Simon Belmont' build. I made up my own arbitrary rules:
I'm using the whip primarily, as well as usable weapons like daggers and firebombs because of their similarity to CV subweapons. I did allow myself to use a sword, especially earlier in the game when the whip was incredibly weak still. But I used some discretion- I used the Astora's Straight Sword, which is described as having belonged to an unknown knight and having a 'powerful blessing'. It's mediocre, but if a Belmont
did own a sword, I figure it'd be holy. I would consider a whip-only run if you could start the game with a whip, but you can't.
Now I've upgraded my whip to a fire whip +7 anyways, so I've ditched the sword completely at this point.
There is a notched whip to be found later in the game as well. When I get that I'll upgrade it to have a special property other than fire, and switch between the two whips when appropriate. I think I'm going to make it divine. Assuming it can be upgrading to anything like a normal plain weapon, which I think it can...
In Dark Souls there are three classes of magic - miracles, magic, and pyromancy. I would imagine that a Belmont would be limited to miracles so I'm only using those.
My armor choices are also based on how much I think I can get my character looking like a Belmont. Right now that means the Crimson Robe, Steel Gauntlets (or the Hard Leather Gauntlets), Black Leather Boots, and the Knight Shield. I'm using the Standard Helm as well, but I take it off from time to time to look more Belmont-y. I'll see if I can take a picture later on. Perhaps other Dark Souls players might have an opinion on what armor would be most appropriate, but I think I've chosen pretty well.

Unrelated, here's a glowing Dark Souls review that I strongly agree with:
Dark Souls is more Zelda than Zelda, more Metroid than MetroidThe author makes a case for why he feels From Software understands what makes earlier Zelda and Metroid titles so likeable, and why Dark Souls does a better job at living up to The Legend of Zelda and Super Metroid than Twilight Princess or Metroid: Other M. I think I want to sign up and post a comment chiming on on why you can add Castlevania to that list.