I disagree, you do need stamina. How else are you going to be able to pick up any loot whatsoever? I put mine into stamina and health evenly. I don't use slow mo because I cannot stand it. I level up my sneak, archery, one handed, smithing, and enchanting. Also pickpocket, and lockpicking just for the heck of it. My character is based off of BBC's Robin Hood. I play imperial, with a hunting bow, and scimitar, "Clothes" (green with black vest), light imperial bracers(bow enchantment), theives guild boots, and ring and necklace with bow enchantments. I do perfectly fine as an archer. I mostly kill everything with my bow, if I decided to not sneak and they charge me of course I pull out my sword but who wouldn't.
I just keep a ring and necklace enchanted w/carry weight increase for if I ever need to haul more loot than usual - which is rarely, never had to put any points in stamina on my archer. I did put points in magicka though, but I was kind of an archer+mage not pure archer.
Loot and gold ends up being worthless eventually anyway. I ended up with over 100k on my most complete character, and had nothing to spend it on.
As a "pure" archer there's not much reason not to stack health.
I think the strongest build for an archer is archery+sneak+illusion+conjuration though. Summons keep things away from you so you can constantly fire on them since you rarely will have to kite. Illusion plus sneak makes you practically a ghost and you'll kill most things before they see you.