Psychotherapist here. I qualified 6 years ago and trained at post-grad diploma level for 3 years. BACP registered and I did my accreditation with them about 4 years ago I believe.
I love the job, it's wonderful to get to work with the most vulnerable parts of people that other people don't often see, and see people improve. BACP offer good cpd opportunities and being a member definitely opens more employment doors. NCPS is rapidly gaining more and more members and becoming a large professional body in itself now though, so this is starting to change.
But, employment options are in general very limited and poorly paid unless you go into private practice. I've done both, I much prefer private work but there's a lot of competition out there so know your target group and make sure you aim for that demographic in all your advertising. There's more work available with children and young people under 18 if that's an area you'd want to specialise in, to maximise employment opportunities.
In terms of training, if you're looking to be as employable as possible, train at postgraduate level (7). Most NHS roles and increasing numbers of other employers are asking for this level of training. That's not to say you won't find opportunities at lower levels of training but to maximise what you can apply for you need a post-grad training. Increasingly, they're also asking for BACP accreditation (MBACP accred status) as there are just so many counsellors out there nowadays. Not sure if you're aware of the scoped framework that most professional bodies now adhere to, but accreditation bumps you into band B rather than C which is also better for your practice.
Personally I've never had a client ask about either my qualifications or my professional membership though, so if you're looking to set up privately and that's it, it's less important to get the higher level training.
Make sure you have a lot of personal therapy first. All decent training providers will insist on this as a core part of training- avoid any that don't as it is THE most important part of the training in my opinion. I've had 10 years- client work will trigger things in you both consciously and unconsciously, based on your own lived experiences and it's important for both you and for them that you have as much self awareness of this as possible prior to starting work with clients, some of whom will be incredibly vulnerable. I'm sure you have already started to look into this, but Google transference and countertransference, unconscious process, projection and projective identification for an idea of what I mean by this. You have to really know yourself to be as ethical in this line of work as is possible.
In terms of actual client work, it is varied! It is intense and full on and I find it saps energy form other areas of my life so I have to be very careful about work life balance now- I need to save some of my emotional energy for my family which is incredibly hard after a full day of client work. If you go into private work, there's more admin than you imagine. Clients will contact you 24/7, 7 days a week so choose your boundaries on this early and stick to them. Make it clear to clients when you're available and when you're not. I have a separate phone for client work to keep my private and work life separate. It works well.
You will end up dealing with crises at times so make sure you are clear on your safeguarding responsibilities and know what you would do ahead of the first one if you're working privately.
Last piece of advice- interview supervisors before you settle on someone and know what you want from a supervisor before you start making calls. I wish you all the best.