Well it depends on the therapy you need.
First of all you must get a fully accredited member of the BACP. Not simply a member but one who has been accredited. This means that they have completed at least 450 hours of educational course with a minimum of 450 hours of practical experience. It also ensures that they have been working as a therapist for over 3 years.
There are lots of people working as therapists today with little formal training. It's worth your while spending some time getting a very experienced therapist.
Psychotherapists would mostly probably not like to be described as counsellors as their training involves a great deal more personal therapy than a counsellor's training and they are usually at masters level educationally.
Psychotherapy is usually a much longer and more involved form of therapy. Often they will see clients a few times a week for many months. Many people can not commit to that amount of time or money.
CBT mostly addresses areas where your thinking is faulty. (ALthough all therapy does really!) It's beloved by many as it is certainly the most easily quantifiable therapy. It's probably the most mechanical of the therapies as it has agreed methods of dealing with a problem. Most useful in dealing with anxiety depressive thinking disorders like OCD etc. People with longer standing issues that involve deeper issues can find CBT too mechanical and find that the therapist doesn't build a strong enough bond to help them find the strength to address what they need
Psychodynamic therapy has to do with your unconscious and trying to sort out what is at the base of the things you do. It can involve a great deal of insight and free association or even the meaning of dream work at times. Mostly they think that whatever is upsetting the applecart now can be traced back to something usually from childhood and by finding you can move forward. Some people have trouble believing in the associations made in symbolism and free association. Some people have trouble believing in the unconscious and see this as the most unscientific model of therapy.
Person centred or humanistic is all about the you. They believe that behaviour is connected to self esteem and how you view yourself. Not the therapist but you. They believe that given the right circumstances that you can suss out what is wrong and move toward the things that will be right for you. This is a very focussed and nurturing type of therapy. It ignores the unconscious and the idea of bad eggs etc and believes in the good in people, any people. Many see this as a negative and inexperienced therapists can be particularly ineffective.
Integrative therapists use two of the above types of therapy and apply them to a therapeutic model. The model has a beginning a middle and an end and the idea behind it is that the therapist wants to move you on from the problems that you are experiencing. They will often start in a person centred fashion and build a very strong bond enabling you to explore your issues. Then in the middle phase they might use some CBT exercises to help you with some of the thinking that you have formed and then move you toward and ending using the humanistic thoughtful model again.
Integrative therapy is very effective but only in the hands of fully qualified and accredited therapists.
Most free counselling nowadays is based on a CBT model. This is because the govt can see results. It is very effective for wonky thinking but not terribly strong for older, deeper issues. It's also a quick and relatively cheap cure.
Please ensure that you see someone who knows what they are doing. Therapy can be very helpful and transformative when received from someone who is properly qualified to work with you.
If you need any further advice inbox me