This is not going to be quick or painless. The problem is that as the bosy loses blood, it loses blood pressure, which slows the loss of blood. The easily accessible veins and arteries in the arms are relatively small, and they don't provide enough flow rate to allow a quick death via blood loss. Think about how long it takes to donate blood, using a vein in the arm - slow, and slower as more blood leaves the body.
The only fast options I'm aware of for this kind of suicide are the carotid arteries, the femoral artery and the heart, and all of these are risky and painful. There are documented cases of people going unconscious in seconds from a transected carotid artery, but failure means visible scarring for certain, and a high chance of damage to other neck structures (damaging the voice box, resulting in muteness, for example). The femoral arteries are bigger, but deeper, and I read a case study about a doctor who killed himself this way - he injected himself with a local anesthetic and opened up one of his femoral arteries with a scalpel. The problem is that the femoral arteries are fairly deep, and accessing them involves cutting through enough flesh to be painful and difficult, along with concerns about permanent damage to the muscles and ligatures in the leg. Finally, the heart obviously requires the most forceful, deepest blow, and would not be at all painless.
The proper way in all these methods is with a sharp knife, not an IV or needles, which brings up the problem that it's harder to cut raw flesh than most people think and much, much harder than that when it's your own flesh. I would seriously advise that you reconsider - this is going to be a lot harder and more painful than you think, and is not a very common method if self-deliverence as a result.