Yes, most people put a lot of thought into suicide, because it takes a lot of thought to actually do it. Most people don't commit suicide the first time they ever think to do it. Most people struggle with their mental health for a long time before they decide to finally do it.
Yes, people think a lot about the means of their demise by their own hand. While we can't always know the thoughts of people who die, the notes they leave behind, combined with the narratives by people who survived attempts on their own lives shows that a great deal of contemplation precedes a suicide.
Suicidal thoughts is not something every one goes through, but it can become a problem for a lot of people. To become willing to kill yourself is a long road. It is not something that suddenly happens like a switch in your brain. Its a dull grinding that slowly chips away at your will to live. The longer it goes the more you think about it and the more you contemplate carrying through with the act. You don't just 'have' the pills to overdose on or the rope strong enough to hang yourself with. It takes time to plan and gather the materials. You have to think about it to do it.
Suicide is not easy. Look at how the body reacts when it is chocking or suffering from hypothermia. The body is designed to fight off death. Accordingly suicide is not an easy thing. Often people that commit suicide have had a number of previous attempts that is presumably because the body is repugnant to the notion of termination and fights off the individual at every pass.