Memory Cards are extremely compact and lightweight but may be costlier per megabyte of memory. Disks are larger and the drives can add size and weight to a camera but each megabyte of memory may be more reasonably priced. Some digital cameras actually do use alkaline batteries, but you'll find that disposable batteries are not very practical. Digital camera functions consume battery life fairly quickly. Rechargeable batteries are far more convenient.
Some cameras come with a battery and a battery charger as well.
How long a charged battery lasts depends on how you use your camera. Some features that you use on your digital camera eat away at the battery life faster than other features. If you have a camera with an internal memory, after taking your photos, the camera will indicate that the memory is full. Some cameras save photos onto flash or media cards. The cards come out of the camera and fit into an adapter that then fits into your 3.5inch disk drive.