It's my father's name, and he was born in the fifties. It's also the name of one of my cousins (from my mom's side of the family), and I think he's in his twenties or thirties.
It doesn't sound hopelessly dated to my ears, and I think if I wanted to use it that wouldn't be a deterrent.
I'm not sure which spelling I prefer, but if I did use it I'd probably spell it Brian, like my dad.