Final answer:
To observe a living amoeba engulfing its food, a light compound microscope is the best choice as it allows for real-time viewing of living cells without the need for staining or a vacuum environment.
Step-by-step explanation:
If you want to observe a living cell such as an amoeba engulfing its food, the most appropriate type of microscope to use is a light compound microscope. This type of microscope is advantageous for viewing living organisms since visible light passes through and bends via the lens system, allowing you to see the specimen. Unlike electron microscopes, which require a vacuum environment and often necessitate the fixing and staining of samples (processes that kill the cells), a light microscope can view the dynamics of living cells in real-time without such preparations.
Regarding the visibility of cell components, cells are generally transparent and their parts are not distinguishable without special stains when using a standard light microscope. However, in the context of watching an amoeba consume food, the overall action of phagocytosis can be observed effectively without staining. Options such as the transmission electron microscope (TEM) or scanning electron microscope (SEM) are not suitable for observing live cell processes because they require a vacuum and can't be used to view living cells in real time.