All of these fears are common and an experienced and supportive therapist will understand and support you in those fears whilst also giving you space to explore them. Its also worth bearing in mind that most therapists will have undertaken their own therapy and so will understand what it is like to be in your position.
There are all kinds of psychotherapy and counselling: psychodynamic, person centred, CBT, hypnotherapy, humanistic, gestalt, integrative, transactional analysis etc. It may well be worth researching some of the different kinds out there to find what feels best for you - some therapies are more cognitive, structured and time bound with homework and assessments whilst others are more relationship based and humanistic, giving you space to explore your thoughts and feelings at your own pace.
It's important to find someone you feel you can work with. Each therapist will have their own unique personality and if there’s something that you don’t feel comfortable about with the therapist then the chances are you won’t feel relaxed enough to open up to them. Many therapists offer a free initial assessment session which can give you the opportunity to find out more about the therapy and also importantly so that you can both see if you can work together - if your therapist feels they can help you and importantly if the therapist feels right for you.
Many people say it's a relief to finally make that first step and to talk about what’s on their mind. To be listened to and heard by someone unconnected to their everyday life can feel liberating and people usually leave the session feeling more hopeful.
Ultimately only you can make the choice to start therapy but once you have then it's a great place to no longer have to make such decisions alone.