There's a lot more to a method than just the time it takes for death.
There are other factors like:
Solo suicide or assisted suicide, Noise, Pain, Discomfort, Survival Instinct, lethality, accesibility, price...etc
The best method for a 68 year old grandma from the US is not going to be the best method for a teen from Liberia. The best method for a wheelchair-dependant person is not going to be the best method for a person without hands...etc
So to answer the question:
Best methods possible:
Nuclear bomb, exit bag, inert gas asphyxiation, decapitation, nembutal, fentanyl, morphide od, c4 on head, shot with a shotgun in the head while you sleep, CO method.
All these methods are relatively quick, painless and lethal.
However. On a more realistic note.
Nembutal is a good one. So is fentanyl. Exit bags with nitrogen, helium or argon are good. CO method is also good. I'd say these are the best case scenario for a solo suicide.
However, the best method depends on your circumstances alone. With the exit bag, you need to be able to find and assemble all materials. Nembutal and fentanyl are illegal from what I know. It also could take a while to die from them. Not if you do extensive research though. If you have no privacy the CO method is pretty much not an option....So you see, you have to decide the best method.
I have chosen the Helium Exit Bag method because it is comfortable, painless and I had not much problems with getting the materials.
[DEPENDING ON YOUR SITUATION AND CIRCUMSTANCES, NONE OF THE METHODS I'VE LISTED COULD BE A VIABLE CHOICE. DO YOUR OWN RESEARCH]