Yeah, experiment, practice; figure out what works best for you. If you ride on the drops, you might try my technique for maximizing stability when riding one-handed - I brace my lower forearm (just above the wrist) against the upper bend of the bar, so I have two points of contact with the bar, i.e. my hand and my forearm.
For more accurate shifting, I like to curl my index & middle finger around the front of the shift lever, with my thumb on the back side. Then I can shift according to my wrist angle, instead of just pushing forward or backward on the lever. This is particularly useful when moving fast, over rough road, and/or while pedalling hard. With this technique, the orientation of my hand is "thumbs down".