I will second Meanwhile's rec. of Ergon grips; I've been using these exclusively now for going on five years ... they really do work. You'll need to experiment a little to get the angle just right, but that doesn't take long.

I will also suggest that you do consider bar-ends, either as part of Ergon grips (there are several models) or in addition to them (that is how my bicycle is set up).

Why? Two main reasons:

1. Efficiency when you stand to climb, and

2. Variation of posture. "Hand-comfort" will mainly come from the type/quality of grips you use, given flat-bars. Bar-ends, though, allow you (on longer rides) to rotate your wrists through 90 degrees -- effectively imitating the tops/hoods positions of a drop-bar. That rotation (back and forth periodically) effectively in turn does have an effect right up through the arms/shoulders/upper back. When combined with their other postural consequence, changing your torso angle (one leans slightly more forward when on the bar ends), muscle tension and fatigue overall are reduced through their use, enabling you to ride longer distances more comfortably.