What magnification do I need to see blood cells?
Just my 2-cents worth as visual add-on to @MattDMo 's answer:


Blood smear showing red blood cells and two white blood cells at 400x. Source: Microscope Master


Human red blood cells 1000x. Source: Wikipedia


Human white blood cells 2000x. The small dots (red arrow) are Diplococcus gonorrhea bacteria (Neisseria gonorrhoeae), each ~0.5 micrometers in diameter. Some of the neutrophils have phagocytosed bacteria. Source: Waynes World


Red blood cells visualized by scanning electron miscroscopy. Source: Pinterest.
Note: for illustrative and comparative purposes only; electron microscopy is not the most advisable method for home use.