Congrats! It a fun camera to play with, and that's the best tip, keep playing! I'll go into a setting, like a ball game and compare Auto to Sports scene, go back and forth and learn which worked better.
Here's my HX-30 trip report from back in July:
Turn on the full display details, look at the histogram, a picture will be overexposed (too much white) if the right edge of the graph has any lines or height.
P mode, ISO 100 anytime you have good lighting.
The lower Aperture "setting" (higher f/) is actually an ND filter (that's a photographic goodie that pros buy as an add on filter). Use that if you can with bright lights in a shot (like sunsets) or to slow down an exposure (to attempt a dreamy waterfall.
If you need a flash for a portrait, Use P mode or the portrait scene and then select SL flash so people are not overexposed.
For panoramic pictures, instead of pivoting your entire body, hold the camera with 1 finger on top and a thumb on the bottom, and with your other hand, press the shutter, then spin the camera as your fingers just created a perfect axis going through the camera. (Otherwise you get too slow or too fast messages if the camera cannot visually piece low contrast scenery together
I usually use the 24mAVCHD in order to capture stills during video.
Remembering my mom's old photographical axiom, pictures look better with the sun behind you.