It should be noted that while you include suicides into your statistics (and suicides make up the greater bulk of firearm deaths), suicides of and by themselves are NOT effected by the availability of guns. I.E., if there are no guns, suicides will not go down.
Suicide is a cultural phenomena. It is not affected by the availability of easy means to kill oneself. If a firearm is not present, self-strangulation via hanging, overdose, falling, etc will be used in. Neatly highlighting this fact are suicide statistics from the UN's WHO.
http://fathersforlife.org/health/who_suicide_rates.htm
http://www.who.int/mental_health/prevention/suicide/suiciderates/en/
Notice that Japan, where obtaining a firearm legally is almost impossible, has a suicide rate that is greater than that of the United States. So does France, Denmark, and Canada. All nations that strictly regulate firearm possession.
Notice that the highest rates of suicide are in former Soviet countries. Places where government corruption and economic instability are high.
Essentially, your not going to keep anyone from committing suicide if firearms are removed. They'll simply use another method.
This is similar to what will happen to murder and violent crime rates should firearms be removed. Criminals will simply use another method to kill. The only difference will be that their victims be unarmed, and unable to fight back.
The method to reducing violent crime is NOT to disarm victims, but to lock up criminals and keep them off the streets. Another method would be to address social issues that cause people to commit crimes in the first place. That is to say deal with the drug and gang problems that are the cause of the overwhelming majority of violent crimes in the US.
It should also be noted that gun control is rooted in racist policies, and that modern gun control is not much different. Historically, gun control was first used in the United States to keep African Americans from owning firearms, first when they were slaves and later when they were emancipated after the Civil War.
Today, gun control policies keep people who are poor from owning a means of self defense. In many areas like New York and areas in California, legally obtaining a firearm and/or the license to conceal or carry one is almost impossible unless you are well connected. Licenses are expensive and difficult or impossible to obtain. This keeps effective self defense out of the hands of many middle and lower class Americans, and is a travesty of justice.