Having been on the design team of several helicopters, the answer is a bit more complicated that Dave describes (although for some manufacturers, their quiver seems to have only one type of arrow, so dave is not totally off base!)
The biggest determinent is the mission, and the needed CG range (longitudinal and lateral), the maneuverability and the flight envelope (especially the negative G).
Almost nobody would develop a new helicopter with a conventional teetering rotor or a lubricated articulated rotor any more, unless the resources were very low, or the mission was very benign.
Most rotors now fall into two groups, the bearingless flex beam rotor, and the elastomeric bearing rotor, both really variations on the same theme.
Only marginal homebuilts use teetering rotors because the whole reason for their existence, low cost, determines that they keep an easily built, light weight rotor head design.