Like ace said, Mateen was cleared by the Feds. So I'm not sure I understand why it would be a good starting point to restrict suspected terrorists from buying guns. What exactly does that mean, btw? Someone who has ever been to the Middle East? Someone who makes phone calls to the ME? Someone who reads Arabic news online? What? Again, you need to be as specific as possible. How do we define "suspected terrorist"? You can't arrest and detain people with no prior history for something law enforcement thinks they might do.
After that, how many times does the suspected terrorist need to be interviewed by the FBI before they are no longer allowed to purchase a gun? Five, 10...40? How did you arrive at whatever that magic number is?
So no, we can't "start" where you suggested because it doesn't get us anywhere. Far too many question marks that can never be defined. These are the pesky things called "details" which dims like to overlook when they want to implement their agenda.
You our do realize what you're suggesting is somewhat akin to banning all computers, or at the very least restricting access to almost everyone, because some users may commit cyber crimes on them, right?