Andrew,
It's good that you're asking all the right questions to arrive at a safe setup.
Yes, you need the WD Hitch and Brake Controller as noted above. Get a Hitch with "built in" sway control like the Equalizer or Reese Dual Cam. The Blue Ox Pro is also getting very good reviews on this site too. You can download instructions on all of them and see what's involved in setting them up. I went with the Equalizer for my new trailer because it was an easier setup on my type of trailer. I got mine for $495 from Tweetys with free shipping.
The purpose of the WD hitch is to return weight to your front axle that was removed when you lowered the trailer fully on the ball. You must return weight to the front axle or you will have a dangerous ride as you found out!
NOTE: Your WD bars must be properly sized for your weight of trailer too so check this out before buying. For instance they have 600, 800, 1,000 lb bars, etc, and even heavier, so get the right ones.
As to the brake controller, the Tekonsha line is very popular. I have their original Prodigy but they've got some newer ones now like the P2 and P2 with a few more bells and whistles. Along with the controller, get the Tekonsha pigtail for your Chevy and the install will be plug and play. The pigtails are around 12-15 bucks.
You MIGHT have to install a fuse or circuit breaker somewhere, but I don't know. Others with Chevys can advise here or check your manual. All of this is not too complicated and you should be able to do it yourself if you're handy and can follow instructions.