VERY slow recognition of Magic Mouse and Keyboard on start-up.

The following will require any USB keyboard and mouse. If you don’t have them, borrow or buy them, they are inexpensive!

1. Connect the USB keyboard and mouse to the computer.
2. Open System Preferences – Bluetooth
3. Un-pair the wireless keyboard and mouse.
4. Turn off Bluetooth
5. Restart the computer in Safe Mode per the directions in How to use safe mode on your Mac - Apple Support
6. Restart the computer normally.
7. Open System Preferences – Bluetooth
8. Turn on Bluetooth
9. Re-Pair the wireless keyboard and mouse.

10. Unplug the USB keyboard and mouse and begin testing the wireless devices again.

Just so you know if you have a wireless keyboard with rechargeable batteries connect it with its USB charging cable.  The cable turns it into a wired keyboard. 

Unfortunately the Magic Mouse isn't as fortunate. But you might be able to boot into Safe Mode according to How to use safe mode on your Mac and see if the problem persists. Reboot normally and test again.