John shares his knowledge of fiber optics by answering your specific questions
What is the most important quality to look for in a cleaver?
The unit's cleave angle specification. This spec indicates how many degrees the cleave will vary from an "ideal" cleave, which is considered to be 90 degrees perpendicular to the fiber endface. A high-end cleaver used for fusion splicing should be able to produce a cleave angle within about one-half degree. A low-cost cleaver used for mechanical splicing should be able to produce a cleave angle within about two degrees.
In a mechanical splice, the more that the angle of the cleave departs from the 90 degree "ideal" cleave, the more space there will be between the endfaces of the two fibers within the splice. However, mechanical splices are somewhat forgiving, since most contain index-matching gel that fills in this gap.
Fusion splicing is more demanding. The cleave angles of the two fibers must match as closely as possible so that the glass will fuse properly.
By the way, if you already own a high-end fusion splice cleaver, you might want to use it for your mechanical splices as well. The cleave angle produced by a precision cleaver results in a splice loss of only about .01dB, whereas a low-cost mechanical splice cleaver produces a loss of about .1 dB