I'd like to shoot live concert photos with my camera. Are there ideal settings that I should be looking for with a small-sensor point-and-shoot that enable me to have a better chance to get good photos from my efforts?
I have a Panasonic Lumix DMC-TZ10.
Shoot festival concerts during daylight hours. Honestly, that's about it.
Theatrical/concert photography is about the most challenging there is, both in terms of pushing the equipment you use to the absolute edge of their capabilities and in terms of requiring every bit of skill and experience you might have as the photographer.
Photography is the art of capturing light. Most concerts don't offer much light to capture and what light there is to capture is changing rapidly and the subjects are usually very animated. So the traditional solution to not much light (longer shutter speed using a tripod to hold the camera still) doesn't work because nobody on stage stands still for 10-15 seconds while you take a picture. The traditional solution to capturing motion (faster shutter speeds) doesn't usually work because there isn't enough light to capture a good image on a small sensor with a narrow aperture. In the end you have to balance the two as best you can AND use gear that allows you to capture as much of the scarce light that is present in the scene in as fast a time as possible. That means fast lenses (wide apertures), larger sensors, and cameras that are highly responsive (fast handling). Most point-and-shoot cameras trade all of that away to make them compact, light, and relatively inexpensive.
Your Panasonic Lumix DMSC-TZ10 has a sensor that is about 1/16 the size of a "Full Frame" sensor. That's roughly 4 stops of light difference in terms of light gathering capability. The maximum aperture of f/3.3-4.9 is anywhere from 1/3 to 1 2/3 stops slower than an f/2.8 lens, and 2 1/3 to 3 2/3 stops slower than an f/1.4 prime lens! So at a middle focal length where your camera is at f/4 you must use a shutter speed 32X slower than a FF camera with an f/2.8 lens! If the pro camera can get the shot at 1/320 second (where it is about 50/50 chance you can freeze the motion of the performers if you time it just right), your point-and-shoot needs 1/10 second to collect the same amount of light. Assuming your camera didn't move at all in that 1/10 second (near impossible at a concert, even your tripod will vibrate with the energy pumping out of the speakers) everything on stage is still going to be a blurry mess for all but the most static of performers.
Honestly, with a point and shoot, it's going to be tricky. Based on your phrasing, it sounds like it's an indoor show. In my experience, the lighting is pretty bad.
So with a point and shoot, I'd advise shooting with a 1/60 shutter speed as the fastest, but lower is possible. You'll want to be close, since camera shake at distance will definitely be a problem. Shoot high ISO, you may want to process in B/W to artify the noise you get.
The other thing to pay attention to is stage lighting. If you can capture band members in that light you can have a nice dramatic shot.
Start with the highest ISO your camera can manage without too much noise ("too much" being entirely up to you, of course). Use as wide an aperture as you can and still keep what you want in focus. Then adjust your shutter speed until you get what you want. Expect to spend a fair amount of the first song just getting to where you can shoot something usable. Practice adjusting your shutter speed quickly because many concerts have shifting lights, sometimes fog, and band members have an annoying habit of moving out of the light.
When you start getting something you like, do what you can to minimize shake. Lean against a wall, brace your arms on a table. If you're standing, pull your elbows close to your body. Anything that will help you keep your camera steady is good.
Watch the performers and try to get a feel for how they move. You can almost always find videos of a given band online so watch a few beforehand to see how they perform certain songs. If you can tell that the lead singer always pops his head back at the chorus, focus on his mic, frame your shot and wait for it. Does the lead guitarist pull her axe vertical to hold that note? Be ready for her. Be prepared to shoot a few dozen shots of the drummer to get one that works. Drummers are the fastest moving and worst-lit people on the stage and they're the hardest to shoot.
Try shooting singers in between lyrics, that's when you'll get smiles and sneers and quiet moments and laughing and tongues sticking out. Mix up what you shoot: get the whole band, get each member individually, try to get shots with two or more bouncing off each other. Note that if you shoot an individual band member and don't need anyone else in focus you can increase your aperture size even more and get more light. I like trying to get at least one good shot from the side of the band interacting with the audience.
Avoid using a flash if you can. It'll be nearly impossible to light all the band members very well, plus you lose the reds and blues and purples that make concert photography fun.
