2) Apply for big companies / public sector. They have massive HR departments who will send you an equal opportunities form. Disclose your disability and ask for support during the interview. That should help them prepare for you - they will also have the budget to support you if you do get the job and require extra help.
3) Build a portfolio. If your CV and Portfolio are good, then your interview is basically "can we work with this person." If people are sufficiently impressed with your work, it won't matter whether you stammer, have dreadful BO, and have a hobby of murdering kittens on the weekend.
4) Speak to your GP and see if you can get help. Speech therapy isn't perfect, but it can help.
Good luck!