Personally, I think a tiered system has some merit. Classify firearms based on how many shots they can fire within a pre-determined time period into 3, 5, 10 tiers. The number is secondary to the point.
New owners can only buy from Tier 1. After X years without adverse incidences, which could range from speeding tickets to felony arrests, they graduate to the next tier. Set the tiers appropriately far apart and you don't have to restrict gun types or magazines or licenses to carry. Instead, your newest buyers are stuck with low danger firearms and gradually prove that they're responsible enough to own more dangerous options.
Selling to someone beyond their tier level is a major felony resulting in 25 years in jail. Firearms are registered and sellers have to provide proof that their weapons are still in their control or records of who/when they were sold.
It doesn't do anything about lagacy weapons but that's a different question for a different day.