Q: iMac not connecting quickly to internet

Let's see where the hangup is.

Open console in Applications>Utilities, check the system log for the date/time of the last Startup and right after that for clues.

Click on the top line we want, Shift plus click on the bottom line we want, CMD+c to copy, then paste the text in a reply with CMD+v

A few dozen lines should be about right, hundreds or thousands won't likely be readable.

Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.

Any change?

Similar issue with my mid-2010 iMac, but only since upgrading to Sierra.  After waking, the wifi connection is not restored until I explicitly select the network from the list (I have waited several minutes).  This did not happen prior to Sierra, and it does not seem to affect my mid-2012 Air.