Your Silverado can pull somewhere around 6800-7300 lbs, depending on its exact configuration. See http://www.chevrolet.com/silverado/specifications/ and click on the "Trailering" tab for details.
The actual towing capacity will be reduced by the weight of anything else you carry in the truck, so figure a max trailer weight of about 6000 lbs. When looking at trailers, first check the trailer weight, which should be shown as both an unladen (empty or dry) weight and a GVWR (Gross Vehicle Weight Rating). For safety's sake, you should assume that the trailer will in fact to loaded to its maximum, so look at trailers with a GVWR of 5400- 6000 lbs and you should be OK.
By all means add a transmission coller. Your brakes should be OK, but make sure the brakes on the trailer are in top notch condition. Trailer brakes are usually only marginally adequate for their GVWR, so there is no safety factor there. Your rear suspension should also be OK as long as you do not exceed the trucks rear axle capacity, which should be plenty for a trailer in this size range. The trailer's tongue (hitch) weight will be 10-14% of the trailer weight or somewhere around 600-750 lbs, which is not a big load for a 1500.
You should have lots of trailers to chose from in this weight range. Light duty (vacation) models of up to around 24 feet may qualify, but something around 21 feet would probably be a better choice. If you choose a fifth wheel model, you can go a bit heavier, as is shown in the Chevy trailer specifications. That's because a fifth wheel positions the weight over the truck axle rather than behind the bumper.