Is it more economical to use hot water before boiling or to bring cold water to a boil?
It might be slightly more economical, but it also might be slightly worse for your health.  Hot water dissolves plumbing (pipes, valves, fixtures, etc.) much faster, and what it dissolves is in the water.

Lead is specifically of concern, particularly with homes prior to 1986 and with infants.  There's a NY Times article that sums it up nicely with sources.