I am a firm believer in LRFD, but I can not argue with the simplicity of ASD. I use LRFD for steel design practically all the time, but usually it is because the majority of my buildings are concrete with only small amounts of steel. I therefore think that if I am going to design most of the building with LRFD (concrete design), I need to design the whole structure that way.
Anyway, I think your best bet is to get your info straight from the horse's mouth and use the AISC ASD Manual.
Sooner or later though, the ASD manual will be so scarce that we will have to use LRFD.