How much would it cost for a new transmission and the labor to put it on

We don't get involved with costs here because there's way too many variables. You won't get a new transmission because the cost is really high. You will get a professionally-rebuilt transmission, a used one from a salvage yard, or yours will be rebuilt. Most larger transmission specialty shops will rebuild a whole series of popular models and put them in stock so they're ready to install in a customer's vehicle right away. They will have all worn and broken parts replaced, and updated or improved parts will be used when possible. The aftermarket industry is really good about coming up with fixes for original design flaws so you may get a better product compared to a rebuilt transmission from the dealer.

Even when a specialty shop has to rebuild your transmission, it will usually cost less than the cost of a rebuilt one from the dealer. The exception is when there is little wrong with yours but it still has to be totally disassembled. Then you have to weight the cost of those improved parts, and decide if they're a good investment when the old parts are still okay. Do you want to replace a perfectly good part just because there's something better available?

As for the labor cost, most shops use a "flat rate" guide that spells out exactly how long each job should take, and it includes variables like your engine size, optional equipment that can get in the way, your specific year and model, and things like that. That way every shop will quote you the same number of hours and only their hourly labor rate will vary. The lowest labor rate might not be the best value if there are a lot of younger, inexperienced people working there. Mistakes can be made, and the shop will take care of those, but that can mean removing the transmission a second time, and that can inconvenience some people. Inexperienced mechanics also will not get the job done in the specified amount of time, but you don't get charged more. Experienced mechanics who have learned how to be efficient and have invested in better tools and training will beat flat rate time and get the job done sooner, but you still pay the same amount. It's similar to paying a set price for a haircut regardless of how long it takes the barber to do his magic.

If you get quotes from two different shops, naturally they won't be exactly the same. You have to compare the list of things that are included. One shop might order rebuild kits as they need them, and another might order kits for popular vehicles in bulk and get a better price. Some shops only buy rebuild kits through the dealer, and for GM products they are going to pay a real lot more for the name on the box. Some mechanics automatically include certain new parts in their repair estimates because they're a common failure item. Other mechanics might give you a lower estimate with the stipulation that part will need to be replaced only if inspection shows it has worn out. You could end up paying more than the original, lower estimate.

As a general rule, the better shops will give you a longer warranty period but they will have a higher labor rate too. The few extra dollars from each job is what helps cover their costs associated with correcting problems you shouldn't have to pay for later.