I think a good beginner system consists of 12" / 1" tops, get the best tops your budget allows, then build your own subs. For the genres named I would look at decent 40 Hz and up, like Cubo 15 or Cubo 18 (or any of the other suitable designs on freespeakerplans). The subs require an amplifier, the tops require another amplifier (or are active themselves), signals separated by an active crossover or sound processor, with a decent high pass for the subs.
After that you can expand and gradually make your system as sophisticated as you like, 12"/1" tops can become DJ-monitors, active 2-way can become active 3-way, etc.