To observe microorganisms like E. coli, a microscope with at least a 100X objective (over 1000X total magnification) is recommended for detailed viewing, although a 40X objective (over 400X magnification) can suffice when using stained samples. Staining is not advised for home use due to the mess involved. For affordable microscope options, eBay is suggested as a potential source. Additionally, a user expressed difficulty in observing Brownian movement with a 100X microscope, indicating uncertainty about the necessary magnification for this phenomenon, typically observed in aqueous solutions.