Hole saws have cutting speeds that should be considered when drilling into frames and doors. I once saw an installer take a $60 (employer-supplied) hole saw new out of the box to drill a hole in a steel door frame. The saw got burned up before the hole was completed. When using a hand drill, be aware of the drill's RPM. Many hand drills can run up to 2000 RPMs, most to 1000. This may be too fast for the saw, depending on the material. Using a bi-metal saw, you should stay under 80 surface feet per minute (SFM) cutting rate in a steel door frame. Compute RPMs with the following (simplified) formula:
RPM = SFM / (.26 x saw diameter)
Example with a 3/4" hole saw: 80 / (.195) = 410 RPM
This number is much slower than the max RPM of most popular hand drills. For aluminum frames and other softer materials, you can go much faster. For softer materials like aluminum, you can use 180 SFM as a good starting number, but can go up to 300 SFM easily. With carbide-tipped saws, you can safely 2x the SFM number.
Use a variable-speed (or geared) hand drill with good grips, use sharp saws, and approximate the RPM with the amount of trigger pull on the drill, especially on harder materials. With metals, put a drop of oil on the saw while cutting. Consider adding a small hole inside the periphery of the larger sawed hole before sawing to let chips escape the cut. The smaller the drill, the higher the RPM, which can be counter-intuitive, so go slow! The same formula can be used for drill diameters.