It only plays a role in avatar creation at the start, and all it does is affect which of their base stats are higher or lower than normal. They're generally a pretty balanced character regardless, and there will be plenty of characters to round out their weaknesses, so don't stress about it too much. If all else fails, go with the default (I think that's what I did).

EDIT: In case you're still worried, take comfort in the fact that I didn't even remember what you were talking about, being more than halfway through the game. I had to look it up to remember even choosing those options.

So it only impacts the player character then?

I was unaware you're actually a unit in Awakening until now, so I had assumed it applied to every one of your units. I can live with it only impacting the tactician, you can get away with flawed luck with high HP.

The safest bets are +skill/+speed and -luck.

Also, assuming you're playing male avatar, it'll also affect Morgan and her sibling's stats as well.