I would suggest to go vit first, then str.
Points in vitality will scale you life as you level "Every Level Up you will gain an amount of life equal to your base vitality.", so the sooner you get more vit stats, the better you situation will be at higher levels.
At low levels, you should be fine without the extra str as the monsters will be easier to kill.
Are you sure Vitality doesn't give you the extra life per level retroactively? The only reason I ask is I tried to test it last climb by starting with str and didn't begin stating vit until level 40 and, and every time I added a point to vit it would give me hp equal to my level.
Assuming it does give me the same amount of hp when applied retroactively I like starting with str first for the first ~10 levels because I don't need any extra hp at that stage, and then I start adding vit until level ~40 so that I get all the defense benefits by the time I really start to need it. And from there everything else goes into str again
