Right time - Right therapist
When you feel you're in the right mind to begin to do something about your situation, it is important that you also find a therapist you feel comfortable with.
All good therapists will do their best to ensure you are comfortable, they will be empathic and will not judge you and they will work in an ethical way. However, we're only human, and we get on with people in very different ways. If you don't like the therapist you've begun working with, perhaps they remind you too much of an ex, or your mother, and although this would be great work discussing this 'transference', sometimes it can be too much at the beginning of the therapeutic relationship. So unless you have the time and energy to explore all of that before you dive into the stuff you actually want to explore, move on, and don't feel bad about talking to a few therapists before you make your mind up.
Finding the right therapist is no different than finding a good GP or a good hair-dresser. You want to feel that they understand you and your needs, and you want to feel as comfortable as possible.
Be aware that an expensive therapist is no guide to a successful outcome. The relationship you build with your therapist is going to have an impact more than any other factor.
If it's not your time yet, you dip in for a couple of appointments and then leave, that's okay. Sometimes we are just not ready! It may be that we are 'doing it' for wrong reasons, or to please someone else. It may take a few attempts over time before you can honestly say you are ready to dive in.