The best way to get familiar with how ratings affect performance is looking at historical data of the players in your league. When making decisions on who to draft, sign, trade, extend, decline, etc., I'm constantly looking at the ratings of comparable players in my leagues and what kind of production those ratings produce. I also look through HOF players and their career #'s vs. their ratings to learn how to spot elite level talent.
But to answer your question:
Hitters Primary: CON PWR VLH VRH EYE
VRH is #1. But various combinations of those attributes can lead to a successful hitter.
I don't pay too much attention to the others. Base-running and speed are nice, especially for high OBP guys, but not essential. OTOH really low speed means more GIDP and fewer infield hits. I don't place any weight on bunting and push/pull. I'd be open to others owners' opinions on them but I've never seen anyone else put much weight into them either.
Pitching Primary: CON, VLH, VRH, P1, P2
Secondary: VEL, GB/FB, Secondary pitches
Again, VRH is #1