Portrait photography is traditionally done with a moderate telephoto lens. For a 35mm camera, for instance, the 'standard' lens is 45 or 55 mm, but a portrait lens might be 90 or 100mm. This gives you less distortion. With a standard lens you have to get right up close to fill the frame with their head and shoulders, and it makes their nose look big. 8^)
Most digital cameras have a 3x optical zoom. And that's enough to get good portraits, zoomed all the way out, or most of the way. Also most digital cameras, even the cheapest ones, have auto focus, which works just fine if you use it right.
There is a class of cameras that are nicer than just a regular digital camera but not exactly 'professional'. Sometimes they are called 'pro-sumer' cameras, sometimes 'super zoom' because they usually have at least a 12x zoom. On the other hand they are a little bigger and bulkier than just a regular camera. The Canon S5 IS is in this category. Also the Nikon P80 and P90. They look like an SLR, and this is a little deceptive because they're not SLRs. But they have a lot of features beyond your 'standard' digital camera.
If you really want to get into photography, you want to be able to set the f-stop, shutter speed, and focus by yourself. The automatic modes work better all the time, but if you really want control over your photos, you want to be able to select these, and to learn how they interact to control exposure, depth of field, freezing or blurring of motion, etc. Most of the better cameras have the option of manually setting these things.
