I very strongly suggest learning the EPs that do an adjacent swap on both sides and an opposite swap on both sides. You can solve every non-parity EP with the adjacent-adjacent alg and U/D turns, so it's a really useful alg to know, and it doesn't require you to swap layers at any point. There aren't a lot of people who know all the EP algs, but you can get quite fast just by spamming adjacent-adjacent (with practice the algorithm takes about a second to perform).
As far as corner permutation, you should really permute both layers at once. There are only 8 possibilities to learn (5 different algorithms if you know how to mirror) and it saves a lot of time over doing them separately.
Have you thought about what you're going to do with parity? You can do it after permuting the corners but this tends to be pretty long. Another option is to do it before corner permutation, which is slightly harder to recognize (you are checking two PLLs instead of two edges-only PLLs) but has a much shorter alg. The thing is, if you want to get really fast, you're going to want to combine the parity step with some other step, and if you do parity after CP you need to learn 50 extra cases, but if you do it before CP you only need to learn 9 extra cases (for the 9 corner permutation possibilities).
