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I found a list of 60 or so (62) "tips" for chess. One of them says "Take with the man of least value, unless there is a definite reason for doing otherwise". Can someone explain the why behind this reasoning?

I believe this tip is referring to when exchanging pieces. Obviously if there is a hanging piece and you could take it with one of many pieces, you need to look at which piece would be in the best position after taking the piece. However in exchanging pieces, you USUALLY want to take with the least valuable piece first because the square is guarded multiple times by your opponents pieces, and if he/she decides not to continue the exchange, you've lost the least amount of material.

2shay