The advice above is generally good - you just need to adapt to your camera, and figure out the best settings changes to make to the camera so it starts putting out shots more reliably and with the look you like.
RAW will NOT help you take better photos, nor will it produce better photos out of the camera...do not even think of RAW at this stage - if you're still shooting a DSLR in Auto mode with a kit lens and don't do any post processing, you're not ready to be worried about RAW, which requires post-processing every photo with skill and knowledge of what you're doing. JPG is perfectly capable of doing everything you need, from family snapshots to full-on professional large prints for sale or gallery display.
You may consider straying from the full auto mode, and trying out the P or Program Auto mode. It's very similar to full auto, but it allows you to take over a few settings yourself to adjust how the camera delivers the shots. Your camera will have a picture settings mode where you can choose different preset styles such as Standard, Vivid, Landscape, Portrait, etc...each one adjusts the color and tone curves for the output and one might work better for you. Also, each one of those settings has a few adjustments you can make within - for example, in 'vivid', you can choose that mode, then within that mode, you can adjust the saturation, color, sharpness, and/or contrast up or down to fine tune the look.
You might also consider switching the metering mode - something again you might not be able to do in full auto mode, but can do in P mode. The camera is likely using multiple or wide metering area, and should have an option for center-weighted metering - which on many cameras is actually more reliable in mixed lighting situations.
Make sure your EV setting hasn't been adjusted - there's an EV button somewhere, and it can be adjusted - or +...this tells the camera to underexpose (-) or overexpose (+)...if your camera accidentally got set to -1 or -2, that could cause all your shots to end up too dark and underexposed.
Just some starting points to consider. Also - even after all that, if you determine that you don't like the way the photos are coming out and no amount of tuning or settings changes help - try changing lenses. It's not always the camera body that gives poor results - you may just have a poor lens. If it's the kit lens that came with the camera, see if you can go to a store and try another - it might be that a nicer lens will give you better results, or it could be that you just got a lemon of a kit lens, and replacing it with another could improve things.