Options for fixing transmission failure

My wife's car has problem shifting into a gear
(automatic shifting) when you first start the car.
With a push or with manual it starts running
however the rpm, shifting and speedometer are a
little erratic. The mechanics say it's a transmission
failure. The options they gave me are replace with
new for ~8k or used one for ~2.8k.
Do you think it's a far price? And what other
options do I have? I saw good used transmissions
on a used parts website for just ~500. So I think
the mechanics I spoke to are overcharging.

Thank you for your replies.