I am one who actually thinks that the Father Brown stories, which get the most press, are the least valuable of his writings. I find the general premise fairly ludicrous even though there are good spiritual points and insight.
Of far greater impact are his apologetic works.
Orthodoxy,
Heretics and
The Everlasting Man are all among the best books I have ever read, especially TEM. Consider that it was TEM that launched Lewis on his path to Christianity.
What's Wrong With the World (WWWW), while not his best work, has some really incisive stuff on how our world has developed - since he wrote it! But it's bound to be unpopular with people who believe our world is perfect and getting better every day.
The Flying Inn, while being a fanciful tale of Islamic standards brought into British public life, foreshadows how some of them are being brought into western public life in general today.
As a master of one-liners, he has a ton of quotations that hit home:
If you believe that there's nothing wrong with the world, that alcohol has no place at all in our lives, or that Christianity should mean whatever you want it to mean, then Chesterton is not for you.
Or maybe he is...
"Eh? Two views? There are a dozen views about everything until you know the answer. Then there's never more than one."
Bill "The Blizzard" Hingest - That Hideous Strength