Although I have not yet found the reasons for the poor performance of El Capitan on my Mac Mini, I have found a workaround that is almost 100% effective.
Early in the boot-up process, the screen displays a gray Apple logo with a narrow gray progress bar below. The progress bar increases in length noticeably for about a minute, but then slows significantly at about the 60%-70% mark. At this point, I press and hold the power button on the back of the computer for five seconds, which causes the computer to shut down. Then I immediately press the power button again to initiate another start-up. I find that it proceeds normally and quickly, and that I no longer get the spinning beachball every few seconds all day long.
I don’t know if it is relevant, by my machine is configured NOT to display a login dialog on start-up.
If you find this workaround to be successful for you, please add a posting here. It may eventually help us diagnose this problem better.
If you have skill in interpreting console messages, I could post messages before and after the forced shutdown. That might also help us diagnose this problem better.
My configuration: Mac Mini, late 2009, 2.6 GHz Core 2 Duo, 4 GB RAM, 500 GB internal disk with 130 GB partition for El Capitan 10.11.3, 1 TB Western Digital FireWire 800 external disk for Time Machine