I wouldn' t worry about the angle at which the arrows stick out. It could be the target material causing that, or varying torque on your grip, at release. What' s important is your group size at different distances and if you' re hitting your spot. Your bow may need tuning or your form (grip) may need to be more consistant.

As for the stabilizer, most hunters are looking for something that makes the bow quiet and low in vibration. Find a bow shop that will let you try a few and then simply pick the one that makes the bow feel best. Balance is also important and it is best if the stabilizer helps the bow to have very little movement after the shot.