Bob, that is an excellent price anyone should jump on. The peace of mind knowing someone did the correct evaluation and calculations is irreplacable. And that is the OP's quandry, who to believe.
LJ, knowing what size ducts you need is hard to say unless as Bob states, one knows all the room dimensions to determine the proper cubic feet per minute air flow. It's best to have someone like Bob do the evaluation and then you have something to judge contractors with.
If your ducts are only metal without insulation, or the insulation is old and 1"or less and the ducts run through unconditioned space like an attic or crawl space, they will sweat, loose cooling and heating thereby reducing the efficiency of the system. Once someone like Bob does your evaluation, you should also follow up and have them write up a set of specs that the eventual contractor will build to and you have to hold them to the specs. Don't trust anything by word of mouth like happened to me. I just built a new home and contracted with a contractor while living states away, to put in the A/C system. They did an ok job but they didn't put in rectangular ducts in my crawl space like I wanted and they agreed to do, therefore I have round ducts and I can't get under some of them. The insulation is 2" foil faced and they put it on so tight it's only about 3/4" thick, it sweats like crazy in the summer A/C months. I'm in the process of cutting all the insulation lengthwise along the ducts and adding a 4" strip of new insulation to allow the insulation to expand to it's 2 " thickness. In the parts I've finished, I measured a 4 degree difference in the outside temperature of the insulation between the thin insulation and what I've repaired. Moral, is, get everything spec'd out in writing and make sure they put it in according to the specs. Check the insulation and make sure when they are installing it that they aren't wrapping it too tight. It's hell fixing it afterwards and I tell myself everytime I go under the house to fix more of it. I'm about 2/3rds finished and pushing to get done before the A/C season comes.
Bottom line, get someone like Bob to Engineer it for you and then use that to hire the contractor and get the job done. In my estimation, most contractors are going to do an ok job but from what I've seen lately, without specs to go by, you are at their mercy. Also, if they do end up installing new flex duct, make sure they don't use flex duct for the main runs, have them put in metal duct and use flex duct to go off to each room. Minimize the length of the flex duct runs and make sure they are supported every 4-6 feet and the strap has a semicircular metal support on top it to hold the insulation up without crushing the insulation because if you don't, that flex duct will sweat everywhere there is a support strap and the insulation is compressed.