I'm playing skyrim again and last time i've played, i've just went full health. And sometimes i've just ran around waiting for my stamina to fill.
How should the health-stamina ration be?
Once you hit level 55, enemies stop scaling up to your level. Level 55 is generally the highest level of enemy in the game, depending on type. So once you hit level 55 and you seem to be able to survive quite easily, you may decide to take more Stamina instead of Health.
The ultimate choice is up to you though. I maxed my warrior character at around 200-250 Stamina.
It depends on your build. If you are playin shield + one-handed weapon its better to have 2:1.5 ratio. With dual swords or two-handed weapon its better to have something like 2:1. But remember, it also depends on your tactics. If you are carefully enough you can take more stamina.
I tend to mostly play glass cannon-like characters (with dodge-move and high damage mods) and thus I mostly go for 1 point in health for every 2 points in stamina.
In the end it's a matter of your playstile.
Do you play a mobile character that relies on speed, evading and landing attacks when you have the opportunity? Then focus on stamina.
Do you play a heavily armored somewhat immobile tank? Focus on health.