Yep, the guys at my LBS told me that you want to be able to comfortably make a fist without feeling too much pressure across the top of the hand. Guess it's a balancing act ...

Nice advice! But what do you do if even the XL gloves are tight? If it is a balancing act then I am still falling over :D !

+1 I was going to say the same thing. This works for me pretty well. Basically when you're on the hoods (which is where I like to be most of the time) rotate each hand around the hood, away from the center, so that, like he says, there is no bend at the wrist. It feels strange but it seems to get rid of the tingling/numbness.

In the drops, you want to hold the front of the bars, where you can reach the brakes, and not the bottom. So you're not supporting weight directly on your hands the way you would do pushups. There shouldn't be a feeling of instant pain going in the drops.
Make sure your saddle is not tilted forward so much that you feel like you have to push with your hands to stay seated.
Practise riding with a fairly light grip one handed on rough roads. Feel like you don't need to squeeze the bars to stay straight.