The video referred to:
The best camera may be the one you have with you, but a little point & shoot will not deliver professional quality photos from many available light situations. Look at your 186, 207 or 217, for instances. The sensor is too small, so the photosites are extremely small so they can fit 16 mpx of them on the chip. As you get into more expensive cameras with bigger sensors, the camera delivers better dynamic range and shadow detail improves. Even with better cameras, for shots like those mentioned, a light is usually placed behind the subject to provide separation of the background. His socks and shorts, and most of her tutu blend into the black background which leaves floating body parts.
Your Canon PowerShot A1400 does not appear to have a hot shoe, so you have the options of trying to control strobes using the built in flash (which would be difficult), or adding light from a continuous lighting system. The inexpensive version of that is a couple of table lamps. You can get dedicated lamps for a couple of hundred dollars which while not powerful will suffice if your subjects stay relatively still and you use short lenses like the A1400 has.
If you are looking for a career and trying to decide what courses to take, look at business and journalism programs with a minor in fine arts.