The Insider app apparently requires a SIM card to be installed to provision the device. I had the same issue on my Lumia 635 "backup" phone. Installed the SIM and rand the app again and it gave me the choice between Slow and Fast. I made the selection and then restarted without the SIM so that I can keep connected while updating. Checked for updates (I selected "Fast") and it took off displaying "Checking for updates..." for several minutes and now it's downloading!
EDIT: Check your time and date. I don't know which phones this is true for but when I start my phone with Automatic time/date set and no SIM it starts with a default date of sometime last year and I noticed that caused a problem with another step in the update/restart process just now. Turned Auto Date/Time off and set the clock and it's continuing.