I assume at the lowest levels, the more LUCK the better. But, I don't understand how LUCK works in acquiring points. From your explanation, it seems that awarded points are based only on fame of the creatures you kill. Can you clarify?
Here's an example using numbers I'm making up as I go...again made up number - fake ones, did I mention I made these up and do not represent game world examples?
Let's say you kill 3 dragons each with 10,000 fame each, this would give you 30k worth of reward points. At 30k points you may have a 1 in 1424 chance to get a reward - pretty low. Luck may bring that down to something like 1 in 1400...still pretty low - but don't forget you've only got 30k worth of points. Let's say after doing a few cities worth of invasions you are upwards of around 300k points. Your odds are now at lets say 1 in 50 (again I'm making up numbers). What luck will do in this case is drop it down to maybe 1 in 10.
So to summarize, luck is going to enhance your chance at getting a minor artifact - especially as you get closer to 1 to 1. Also remember that you roll every time you kill a creature so maybe it is really your lucky day and you may have the points for a 1 in 300 shot and actually nail it.
The major point being there are a lot of opportunities to roll for artifacts and your progress is tracked throughout so the more you do, the more you get!