Here is a summary of hitches for safe towing.  Which would I have to have?

Frame mounted receiver hitch:  for use with pull type trailers, this hitch provides a stable platform for many types of pull trailers.  It is mounted to the frame of the tow vehicle.  This is the most popular type of hitch and is a safe system if used properly.

Bumper hitch:  for use with pull type trailers, this hitch is mounted to the bumper of the tow vehicle and rated for a certain weight.  Some of these hitches are rated to 10,000 lbs.  Most bumper hitches are factory hitches and are not rated high enough to tow most larger two or three horse pull type trailers.

Equalizer hitch:  used with a frame mounted receiver hitch, this is a torsion system.  It spreads out the downward forces to equalize them between the tow vehicle and the trailer.  Because each tow vehicle and trailer is different, be sure to check with a trusted expert when selecting a hitch system for your vehicle.

Sway bars are part of the equalizer system.  These help augment the equalizer system for more stability.  For larger trailers, there are additional sway or friction bars that are appropriate for a particular trailer.