These should be standard fare in most digital cameras. If so, get a camera with a burst mode of one shot per second or faster. Then select a model with removable memory and buy extra memory cards. Though the feature is standard issue on their more costly cousins, few low-cost digital cameras can display images on your TV set. If this feature is important to you, make sure the camera you buy has video-out capability.
Digital cameras are notorious for eating lots of power.
You will save a lot of money in the long run. You might also want to buy an AC adapter if your camera doesn't come with one. Low-cost cameras aren't for everyone. So don't try to stretch your camera's capabilities. Get as much of your subject and as little unnecessary background as possible.