Most Helpful Guy
I think that they are both quality important. You can have chemistry and be totally incompatible. And you can be totally compatible and zero chemistry. You need both for a relationship
Most Helpful Girl
Without compatibility, what good will chemistry be? Maybe good if you want to be friends with benefits because good chemistry more often than not leads to great sex but not much more.
What good is being compatible but having zero chemistry? Good if you want to be friends I suppose, but not so good for a romantic relationship.
As for which one I seek out first? Hard to say. Sometimes you'll seem really compatible from the get-go, only to have them show their true colours as time goes on proving otherwise. Chemistry I guess is pretty hard to fake, but for many people doesn't become apparent whether it's there or not until they've been together for a while.
I just go with my gut. If it feels right, I'll go along for the ride.
(... no pun intended? :/ )