What is the best way to translate “please choose”: “пожалуйста, выбирайте” or “пожалуйста, выберите” and which aspect should be used with imperative in general?
Imperfective aspect is about state and perfective aspect is about state transition.
So if you are talking about the outcome of a single action ("please pay"), you would use perfective (пожалуйста, заплатите), because what you really want is to make an incomplete payment complete (state transition).
You could use imperfective here as well (пожалуйста, платите), but this would mean that you are more interested in seeing the person paying rather than obtaining the result. For instance, if a patron is waiting for a POS terminal to get fixed and you ask them to retry their payment, пожалуйста, платите would be the correct form.
If you were talking about the state of things ("please pay your bills on time"), you would use imperfective (пожалуйста, платите по счетам вовремя). This would mean "be a good person and organize your life so that you never have overdue debts".
If you said пожалуйста, заплатите по счетам вовремя, this would mean "there are a bunch of bills on your desk, please, at least this one single time, make them paid before they expire"
It is also important to add that the perfective imperative sounds quite rude in some verbs because it is focused on obtaining a result. It normally happens to verbs related to position and motion.
For example, "сядьте" would sound rude and it could be used in court: "Подсудимый, сядьте" (Accused, sit down, please), while "садитесь" is the polite form used if you have guests at home or if you come to an office: "Проходите, садитесь". (Come in and have a seat, please) As you can see, the situation is the same for the verb "проходить-пройти", the imperfective aspect of it is the polite one. Some other verbs that work like that are: "ложиться-лечь", "вставать-встать", "раздеваться-рездеться", etc.
The case of "пожалуйста, выбирайте" and "пожалуйста, выберите" is similar. The first one sounds more polite because your interlocutor gives you time to choose, it is a process, while in the second one you have to choose immediately.
As for google, the initial estimate of the number of matches can be overestimated by orders of magnitude. In fact, google found 270 matches for пожалуйста, выбирайте and 220 matches for пожалуйста, выберите (the initial estimates were about 250,000 and 1,000,000).
As for your question, if the action is simple and one-time, (i.e. choosing a payment method), "пожалуйста, выберите" should be used.
No, this is not an exception. Why do you think it should be?