What would you say is a good amount of potions for a guy who does not use restoration and then for a guy uses restoration? For the weapon and armor, are you saying the only time I can loot armor and weapons is during Helgen?
My non-magic character usually carried around 9 minor healing potions, or 5 of the stronger ones. It adds a bit of challenge to the game, but that's a part of the realism.
As for Helgen: my characters tend only to take the armor and weapon they're given (either Stormcloak or imperial), plus the Mage's robes from the torture room. That's it.

But in all honestly, you should play how YOU like. That's the best way to play!