Hiya,
A very long time ago, and it's a long time since I left the profession, so this may be out of date but as far as I know the following is still true;
ICAEW is more prestigious than ACCA; the 'finished article' is much the same but actuallly getting there in ICAEW is/was rather harder. Both routes produce Chartered Accountants which ATs are not. Big money difference, although AAT is rather more highly regarded (and demanding) than it used to be. Look on it as the equivalent of 'legal executive' qualifications in law. CIMA is an excellent choice for some career paths, but a large source of employers always used to be the public sector. At present, expect opportunities there to be essentially nil, and ex public sector employees with experience filling other vacancies.
Other than foundation stages, or courses that exempt them (such as degrees and the old 1 year Accountancy Foundation Course), you must be employed be to even start studying either ACA or ACCA as both require several years on on-the-job training and experience. That means, incidently, a full time job - you'll get leave for any study courses away and exams (and maybe online tutrorials these days), otherwise studying is done in your own time. If you start off with a college course they will have the machinery to help you look for a job, and 1st Class graduates from the best Unis will be actively head-hunted, but otherwise its up to you.