The doctors that quoted you 2000 is because they will work inside existing hair which is dangerous, and I don't blame them at all. You will see a big difference with 2000.
Realistically though you would need 3000+ to get full density. But you will need a really experienced doctor, willing to take the risk - cause there is one. Get a quote from Asmed in Turkey he is most of the times willing to take the risk.
Either of the above will make you happy I believe, final choice is on you. I if I was you and since you are young and I believe you will have another one in the future I would be conservative.