Number 1 is completely insane.
What exactly is "mental illness" or "mentally ill?"
How do you forbid someone who suffers from, but hasn't been diagnosed as "mentally ill" from purchasing a gun?
What is the threshold for "mentally ill" and who defines it? Would someone who is paranoid that the government is going to take over their freedoms if they don't have their military grade guns/weapons qualify as mentally ill? It certainly does in my book. I consider that delusional thinking.
The Centers for Disease Control estimates that 25% of adults live with some type of mental illness and that 50% of the US population has a mental illness at some point in their life.
Does your proposal also mean that if someone in your household or family have a mental illness that you are prevented from having a gun as well? Remember, other members in your household will have access to the guns even if you aren't mentally ill. The Sandy Point shooter was mentally ill, his mother wasn't; he shot up the school with her guns--access to those guns would be totally legal under your proposal.
Finally, the vast majority of people with mental illness are not violent at all. In my estimation, stripping a person of their 4th Amendment Right to due process is far worse than stripping people of their 2nd Amendment Right to bear arms.