You didn't do anything backwards. Far easier to get the right truck if you know the trailer.
Look on the weight plate and find the pin weight and then compare that to the weight ratings of the truck. Make sure to add 20-30% to the pin weight to account for loading stuff in it.
At 16k lbs, you are probably in 1 ton dually range and if you are going to see any mountains, a diesel makes sense.
Nothing in this size range is going to get 30mpg but unless you are limited to flat land towing, you likely want to move up to the diesel for power not efficency.
