(following up on my own message)

One thing you might want to try is to go out with someone more experienced w. STI shifting who could ride your bike up and down a few hills to see if he/she has the same problems you have - that will tell you either that the shifting is misadjusted, or, if the other rider does not experience those problems, you'll know that you need to work on your shifting technique.

Be patient with yourself, start out on the flats and once you can shift smoothly without chain rattle on the flats, then start working on the hills. You'll gradually learn just how much pressure you'll need to put on the lever under various circumstances, and over time it should become second nature.