How long could it take to buy a pistol or shotgun in your area?

In Australia !

Background check with Local, State & Fed Police.
Letter explaining why you want a Gun Lic.
If ( 85% of the times your request is turned down ) you pay $435 for a 16 hrs course ( 4 x 4hrs ) to assess if you are fit to hold a Lic.
You MUST report to the local police every 6 months with you gun/s for inspection
The Gun/s must be housed in a fireproof Cabinet mounted to a concrete floor in 6 places, it must be inspected by the police.
You also need to do a refresher course every 3 years

Fill out the ATF form takes about 5 minutes and then they run a background check so maybe 10 minutes total.

I don't know. I bought my shotgun 20 years ago at a Walmart and it didn't take long. Maybe an hour.

idk not long with the proper paperwork

As long as it takes to pay for it and fill out the paper work. In free states , with your concealed carry permit ( FBI back found check already done) , it’s a simple transaction .