That transmission shop is a joke.
They should have at least test drove the vehicle to confirm the complaint.
I’d be looking for another shop.
As to a replacement:
That would depend on a few things..
The overall condition of the vehicle … IE engine, brakes, interior, body.
You have to decide if it is worth the investment and if you will be able to drive the car long enough to make it worth while.
If after a transmission replacement, your still having to replace brakes, or ball joints, engine equipment.. it can turn into a money pit.
So best to determine its overall condition fairly.
A salvaged unit is a gamble.
You usually don’t know what mileage or condition it is in.
A decent salvage yard may offer some type of replacement warranty if it is defective, but is extremely limited in the amount of time.
Also if it fails outside the warranty time limit your stuck paying for another along with the labor to install it again.
On rebuilding your existing transmission:
This will be costly to be sure.
Also, you’ll need to find a quality shop who knows what their doing and offer a decent warranty on their work.
the third option would be to get a re-manufactered transmission.
Again from a good source.
Some can offer free replacement on a defective unit and will reimburst some of the labor costs if it needs replacement after install.
Concerning doing it yourself:
If you do the research on the ” How To ”
If you have the skills required.
If you have all the tooling required and have a safe place to do the work.
Yes you could do the job.
If not, this isn’t like adding anti freeze or changing a head light.
Doing this install incorrectly is a very expensive learning experience.
In which case, again I would search for a qualified shop.