I use 20 or 30 volume, if I am going to be applying it straight to my scalp. They suggest 20 volume if you have a very sensitive scalp. The bleach is going to irritate your scalp no matter what, but if you think you can push through it, go for the 40 and make sure you keep it on long enough to get past that yellow stage. Wrap your head and apply heat to speed the process up.
You will also need lightener. I recommend any variation of Blue. Prism lits Blue is pretty good. Its a powder and don't worry about amounts, just put all of a packet in and all of a bottle of bleach. Apply to the back of your head first and work your way around. The top of your scalp is the warmest and will start to lighten faster and you want to give yourself a good amount of time.
Things you will want to have with you at hand: A wet towel, to wipe off the bleach that may get on your skin. A plastic bag, to put over your head after you are done. Something to rake the bleach through your hair. Don't use your fingers. Maybe even a second set of hands. There will come a point where you will wish you had someone to access how well you've covered your head and will need them to finish the job.