Guns should be restricted to some extent. I think people should be allowed to have them, but only with a psych-evaluation, and I think allowing people to buy fully automatic weapons is a bit much. Maybe have a re-evaluation every couple years, and thoroughly document gun purchases. That way, if someone's mental state goes way downhill, their weapons can be seized before they do something horrendous.
There's a reason for the Second Amendment, and so I think stable people should be allowed to bear arms for their own defense, recreational hunting, etc.
And you think that if guns are taken away, the suicide rate will just go down?
Abso-freaking-lutely.
In the UK, the most popular suicide method was carbon monoxide poisoning by oven gas. Eventually, the gas used dropped in its CO content, and suicide rates dropped correspondingly. Other methods of suicide became slightly more frequent, but the overall rate fell dramatically.
http://www.crisis.org.cn/UploadFile/ReadParty/10-Restriction of access to methods of suicide (E).pdf
A lot of times, taking away the easiest means of suicide will cause the person to question whether this is the right decision. As a result, they'll live.