Swaying and avoiding accidents. Help!

I was reading through the old pages and found one about an accident with a TM and now I am a little scared... :'(  Some people told this guy "Hank" that his 2720 was too much for his truck. Well, I am planning to use my Toyota Sienna Mini van to tow my new 2720... It has a 3,500# rating. If necesary I will put everything in the van so the trailer doesn't get heavy. I also be happy to get all the other things that make it safer but I don't understand the difference between all the devices I keep reading about:

a sway bar
an equalizing hitch
a weight distribution hitch

We are planning a trip from Florida all the way to Colorado and back. Am I putting myself in danger??
I would be sooo disapointed if I can't take this trip, on the other hand I don't want to be irresponsible  :-[
Thank you for any advice...
Allie.