After a clean install of Windows 7 for the sole purpose of upgrading it soon after to Windows 10 I've encountered an interesting Windows Update issue: Windows Update screen became stuck on "Checking for updates..." message.
Issue was already reported in many places, for many different Windows versions but none of the solutions worked for me except the following:

1. Directly after upgrading to Service Pack 1 or after installing from SP1 (refresh) media, installer is stuck on "Checking for updates..." and svchost (netsvcs) is using 100% of one of the CPU cores (for 2 cores 50%, for 4 cores 25% etc.). Installing KB3102810 will help, this update will allow continuing with updates.
2. After most if not all updates have been applied and Windows 10 upgrade is available (tray icon) - update is stuck again, same CPU usage of the same process. First thing to do is fixing windows updates database using a Windows Update Automated Troubleshooter.
3. Last resort solution is to use Windows Repair Portable tool. After running Repair_Windows.exe, selecting Repairs -> Open Repairs unselect all and select the following options:
   • 03 - Reset Service Permissions
   • 04 - Register System Files
   • 05 - Repair WMI
   • 10 - Remove Policies Set By Infection
   • 17 - Repair Windows Updates
   • 21 - Repair MSI (Windows Installer)

   Next click "Start Repairs". After reboot the svchost Windows Update process should be unstuck.

Hope it helps.