In Network Preferences:
Set location to Automatic and Configure to DHCP
Turn off IPv6 in Advanced
Sometimes temporarily turning on Broadcast Name at the router can cure problems but this is usually if Macs cannot find the router at all.
Check that you are connecting to your router and not another one.
I followed your instructions.
Nevertheless, the problem is still there.
Being in the networking settings, now I can see that when the iMac wakes up, Airport is looking for a connection, finds my router, and gives an IP-adress.
In de upper part of my window I can see the Wifi sign showing 4 black bars. After a while it shows only 2 bars, and it stays like that. Then the connection to the internet is very slow.
Switching on and off airport several times gives me the 4 black bars again, and then it stays like that. Then I have a good connection and I can go smooth on the internet.
I don't know for sure because my iMac makes connection with my router, ... it works fine for about 10 seconds, and then falls back to the connection with only 2 bars.
For me there is a software problem related with the sleep modus of my iMac.
As a test, I am going to use my computer for a few days, without putting the iMac in the sleep modus.