Let me start with the general question:
Consider the following situation. I want to take a picture of a particular object (that is, not a scenic shot). I can alter my distance from the subject and I can use the zoom on my camera. By altering both at the same time, I can keep the subject the same size in the picture but take different photos. My question is: what changes as I do this?
The obvious answer is "depth of field". So I'm really asking about what other effects I should be aware of.
Background: I've recently upgraded from a (decent) compact camera to one of the micro 4/3rds range and been experimenting with the new-found control over my photographs. Fairly early on, I learnt about "depth of field" and enjoyed taking some photos exploiting variations in that. The photograph that I'm currently trying to take is of a water drop splashing in a puddle (I've a fairly constant source of this due to a leaky gutter!). I've gotten a fairly decent photograph just by taking it on standard settings, but I'm curious as to whether or not I can do better. Obviously, taking the shot with as fast shutter speed as possible is the main thing to do, so I'm particularly interested in whether varying the focal length affects the range of shutter speeds, but I'd also be interested in other factors that are affected by focal length.