The door sticker DOES NOT tell you how much you can pull; it posts GVWR, not GCWR.
Your truck is rated to tow at least 6000lbs, maybe more depending on cab configuration, 2 or 4 wheel drive, axle ratio, and engine selection. Look in your owners manual in the towing section for the GCWR (Gross Combined Weight Rating) for your truck configuration.
You will take the weight of your truck (with driver and passenger, and anything else you plan on carrying in the truck, fuel) and subtract your truck weight from the GCWR. The number you get is your maximum trailer weight.
Also take note of your GVWR to see that you don't go over that number, as well as your rear axle rating to see that your tongue weight is not too much. You will benefit from a load distributing hitch for a heavy tongue trailer.
I would say that you would want a trailer under 6k pounds. You don't want to run your truck at the max. Besides, you need to factor in weight of water, food, bedding, ect. A rule of thumb is to look at the GVWR of the trailer in question. If it is above your maximum trailer weight (that you figured out earlier), then it is too heavy.
You could safely tow a trailer that is in the mid 20' range. Actual length depends on trailer options, and what the trailer is made out of (you can get aluminum framed trailers that weigh a lot less).
Have you decided on a bumper-pull or a 5th wheel? I prefer 5th wheel (they pull and ride better). If you have a short bed truck, you may have clearance issues trailer-to-cab. They make hitches and 5th wheel adapters that move the trailer away from the cab to help with this.