The problem is that the more a JPEG image is compressed, the more detail and color fidelity it loses. Some cameras use maximum compression to make room for more photos. Others give you a choice of compression ratios. With lower compression, you'll be able to store fewer images, but the quality will be higher. If you can afford it, get a camera that lets you decide.
Digital cameras are slow, period.
They can take anywhere from five seconds to half a minute to store each picture once you've pushed the shutter button. So don't expect to take rapid-fire sports shots. On the other hand, five seconds is a lot better than half a minute if you're taking candid photos or have people waiting for you to shoot their pictures. If speed is important, choose a camera that processes photos quickly. Digital cameras eat batteries alive.