CELTA and Trinity are standardized and they have to be good to keep their certification. There are also many other magnificent courses all over the world but sadly they don't command the recognition of the big two: you really have to go with one of those if you are interested in getting a job easily.
Yes, choose a place where you won't be paying through the nose. London is too expensive unless you have a friend to stay with.
Consider the question of which country you are going to teach in. If you plan to stay in Europe, there's no point in spending your precious CELTA hours on a course where all the other teachers will be working in China, and want information about how to teach the alphabet to beginners. Also, check with the school about how many people from different countries are going to be on the course. Now and then you get a group of peeople who want to do the course together and will "drag" the course's focus (despite the trainer's best efforts) towards the problems of their particular school. Also, if you do a course in a particular country, that country's grammar and vocab, particular problems, and school system will dominate the course. Finally, a course that is done abroad will often have foreign teachers doing it. Ask what level of English is required for foreign teachers. The minimum demanded by Cambridge and Trinity is IELTS 8 but this is a level of English where teachers will still be making English errors (though not many.) It can actually be useful to do a course with non-native speakers but there's a down side too: ask the school, and hopefully you'll get an idea of how honest and blunt they are.
Finally, get some feedback. Find out how many people have failed the course in the last 6 months. (Ask the school, and then write to Cambridge to confirm it. There IS a central website for CELTA.) Ask for the name of someone who completed the course successfully 3-12 months ago, and then email them and ask if they would take that course again, and if there are any trainers that weren't up to scratch.
Trinity and Cambridge are both good courses. Do the pre-reading in advance so that you can get the maximum out of the course. Ask lots of questions. Enjoy yourself!