For basic physics (collisions and dynamical behaivior) ANY physics engine you mention will do that.
The difference is in the details. What exactly do you want the physics engine for? Havok is OVERKILL if you are doing anything but highly intensive and high object count projects. Their demo at GDC 2003 had hundreds of ragdoll biped models falling down (as if dumped into a mass grave) to demonstrate it's power; Newton and 3DGS can acheieve the SAME effect, just not with hundreds of models.
Newton is more stable but 3DGS has more support. Newton is an independent project by less than 5 people (?) and thus it's future is as strong as the comitment of said team. 3DGS obviously has a stronger development base and I don't suspect they will drop PE development in the near future. (in theory anyways)
So, here's my advice. Forget Havok. Too expensive and too powerful for what you want to do most likely.
I use the 3DGS engine and while it's buggy still, I have used it with great success and it looks great when it works.
Use the newton engine if you want (for the moment at least) a more seamless experience. I don't use it, but the buzz has it that it is more stable than 3DGS PE.