Training Courses
I have just passed through the BAe College at Cwmbran and an ex-mil controller so feel qualified to speak on this subject.
The costings mentioned are about right and self-sponsorship would be a logical route, but only with some concrete job offers in your back pocket. Failing that, you would need to take a risk and start training, possibly with no reward.
The good news is that there are plenty of slots for qualified student ATCOs once qualified in a particular discipline. However, SATCOs would normally expect an ab-initio student to show some commitment and self-sponsor the first controlling qualification. Some SATCOs might even insist that you train on the job for your operational rating without pay after your completion of ATCO college. These tactics are to de-risk their employment of you as an unknown quantity. So, be prepared to negotiate hard when the time comes and you might need a quite a wedge to see you all the way through. Of course, the wider you are prepared to travel for your new job the more choice you will have regarding the schemes you can negotiate for employment. My advice would be to know the demand at each airport before wading in.
The ATCO courses at BAe and ASTAC are extremely testing even with a sound prior knowledge of aviation and the appropriate aptitude. These courses are very intense and assimilation of the controlling task has to happen rapidly as there is a series of accumulated summative exercises as one progresses. (Fail a summative phase and it is all over - I am afraid) My advice would be to determine that you have the necessary aptitude at the earliest stage. This can be tested at ASTAC or the BAe College for a fee (Around £250 - I think, but check). Also, before starting training you should ensure you are medically fit because you will be wasting your time and money if you are not. Initial medicals are carried out at the CAA Safety Regulation Group HQ in Gatwick South. (Look at the CAA website for details).
The normal route (dictated by general demand for ab-initio controllers) is to complete a compulsory basic theory course before going on to complete aerodrome (ADV/ADI) and then the approach courses (APP and APS). These latter 2 courses would probably follow a few years after your ADV/ADI when you have consolidated as an ADV/ADI ATCO. Normally, the APP and APS courses would be sponsored by your airport employer. As to whether ASTAC or BAe is best. My impression is that they offer similar results and, often the instructors are contracted to both colleges. So, it should really boil down to cost (ATC tuition + food and accommodation). Both colleges will help you out with costings.
Being an ATCO is a great career, but it ain't a walk in the park and the training will be character-building. Success will, though, provide you with a great sense of achievement and, in the main, the best bunch of workmates you could wish for. All the best. I wish you well on your quest.