Update 8/16/16: The Windows 10 Anniversary Update has begun rolling out for Windows 10 Mobile.
The Anniversary Update includes additional features and improvements for your Windows 10 phone.
Download (April 2015 servicing stack update): For the record, here are the steps that fix my problem (32-bit Windows7 SR1) that stuck at "Checking for updates" or "Preparing to install".
(1) run "net stop wuauserv" from to stop Windows Update service; (2) download and install "April 2015 servicing stack update" (Windows6.1-KB3020369-x86.msu") mentioned in this answer; (3) download and install "Windows 7 SP1 Update Rollup" (Windows6.1-KB3179573-x86.msu); (4) download and install the "Windows Update Client Update" (Windows6.1-KB3172605-x86.msu) mentioned in this answer.
you can also search for them here: catalog.update.microsoft.com/Search.aspx? Change the KBXXXXXX to the real KB number like catalog.update.microsoft.com/Search.aspx?
Now install the SUR Tool package, this is a big package and will install many updates along with cleaning up and repairing the Windows update store.
It will also cut down on how many more Windows updates will need to be installed later.
TL; DR: install support.microsoft.com/en-us/kb/3102812 and support.microsoft.com/en-us/kb/3173424 , reboot and re-run Windows Update.
To be able to install the update you first need to install the April 2015 servicing stack update for Windows 7 and Windows Server 2008 R2 update (again, stop WU service before trying to install the MSU).