Being deaf is not a disability, it’s a communication barrier. Finding a specialist driving instructor who has already overcome this barrier will make communication easier; some instructors are fluent in British Sign Language (BSL) and this will be a definite advantage if you sign. If you rely on lip reading however, finding a good Deaf Aware driving instructor who is aware of your needs and requirements will help.
There is no reason why a deaf person cannot learn to drive in either a manual or automatic car; an automatic may be easier but if you pass your test in this type of car you will be restricted to only driving automatics, if you pass in a manual you can drive either. If your driving instructor has access to both manual and automatic cars you will be able to try both and then make a more informed judgement about which you prefer.