Haha... I've asked my PI this before and the basic response is literature precedent and experience determines which you use right off the bat.
In general if you can get away with using n-BuLi, use that. Its what I use for my metal/halogen exchange reactions, transmetalations, and simple deprotonations. The only problem I have had from n-BuLi is it can act as a nucleophile.
t-BuLi I only ever use for ortho lithiations or other very high pka deprotonations. It's not nucleophillic to speak of but substantially more basic than n-BuLi, which can be good or bad depending on what you want to happen. Also it is far less forgiving to mistakes in handling or accidents like a needle breaking.
Sec-BuLi seems to be used more rarely and usually for very specific variations of reactions. For example there are report in the literature of doing o-lithiations with benzoic acid which can then be reacted with various electrophiles, something I don't think you can do with t-BuLi though I have no understanding of why.