Lots of players are now using the cross handed putting stroke because it keeps the putter head low and does not allow for a lot of break down of the arms and wrists in the stroke
Placing your hands on the grip is imporartant because your grip strenth controls the clubface so let your hands fall to your sides and allow the club to fall into your left hand naturally the way the club manufacturer designed it
Hitting the sweet spot of your putter has three advantages, it comes off the face more consistently, with more energy and has over spin instead of side spin