If you are unmarried then you can specify your wishes in your will, however, the Coroner/ social services / family courts will look at the request and consider what is in the child's best interests. If the guardian you chose is a complete stranger to the child or is unsuitable in some other way (eg history of domestic violence) then your wishes may be overruled.
Your partner can apply for parental responsibility, either now or after your death, which gives him/ her responsibilities toward the child, to pay for upkeep if necessary and oversee upbringing/ education, gives the right to consent to medical treatment if the child is too young to consent themselves, but that does not necessarily guarantee access or custody.
That application can be contested or uncontested.
If you wanted your appointed guardian to have equal status you could ask them to apply for parental responsibility now, although that is a big obligation to take on now, unless you have good reason to believe that you are not going to survive until your child is an adult.
It is definitely a good idea to consult your child, if they are old enough to understand, and obviously the person you would like to be a guardian should agree.