I've found investing in stamina to be pretty underwhelming on my 2 - Handed warrior character. You don't need all that much in my experience, just enough to get in 2 or 3 power attacks in a fight as it's unlikely many fights will last beyond that point. If you do happen to need more in the rare extended boss fights, well that's what potions are for. You'll be swimming in +100 and +150 stamina potions before long if you clear out a few dungeons/bandit camps.
I wouldn't bother with more than 200 total stamina myself on this type of warrior character, but I suppose it comes down to how well you can get a feel for the ebb and flow of a typical combat. Say a max of a 4:1 ratio for me, anything more than that seems wasteful as most things won't live long enough for a lack of a stamina to matter much. Besides, not being able to power attack because you're out of stamina is a lot less of an issue than not being alive because you're out of health.

A little magic can be useful for warriors as well btw, so unless you're doing a strict warrior, anti-magic role playing character don't just dump all the points into health. A two-handed weapon using warrior who can also summon an antronach or quickly gain some magical armor in the midst of a tough battle is a much more deadly character.