I use a lot of different methods, but I suppose I'll just list what I can.
1) *orient edges/start my cross or block (I restrict F and B quarter turns, so that my whole F2L is RUL[D])
2) finish cross or block, and get a good idea for my first pair (I usually attempt to spot and follow an edge that will end up in the U layer after all of my cross is done, and spot the corner after)
3) finish F2L minus a final slot (Because my edges are all oriented, I multislot and use mixed pairs)
4) **use final slot to influence corner orientation (try for T, L, U, or skip)
5) ***COLL, or, if I recognize it, ZBLL (I also know the PLLs except the G perms, which I should learn, and a lot of CLL/ZBLL cases that I use in various situations.)
6) EPLL (With my COLL, I generally aim to fix at least one edge, so that I get 3 cycles, or the H perm. I hate the Z.)
* If the cross is readily apparent, if the orientation case sucks, or if I can see a perfect block start, I just go with that and orient edges using my first three pairs.
** Sometimes, I finish the final pair to get a Heise finish. Those are great.
*** I get a lot of fake ZB cases these days (1 setup turn to make a COLL case into a Y perm, that sort of thing) I also manage a bunch of extra Heise style finishes this way with corner commutators.
This is all assuming I'm going to do layer by layer. I see a fair number of Roux starts that I go with, too. I like the method a lot. Just need more work with it. I really should get my CF solutions up to par...
For Roux solves, I look for a good way to make my first block during inspection. I mix blocks a lot, and very rarely finish one entirely before starting the other. I like to use my pairs to orient edges and corners early if I can, so that I have less to do later. With my final pair, I generally fix the center orientation, so that during my COLL or CLL case (I use COLL to preserve good edge orientation cases, or CLL to get a second chance with ones I don't like) I can recognize edge orientation and be prepared.
When I get to the corners step, I can go many ways. Often, I'll have F2L done, and finish with a CLL/OLL case and go from there. Sometimes, I'll notice a nice way to make a block, and finish with Heise. Generally, I use COLL to keep my edges the same and finish corners.
For edges, if I have DB or DF done early, I know the cases to orient the edges, and I know a fair number of L5E algorithms. Special cases are great. If I have a normal orientation, I keep an eye on UR and UL while I'm flipping, and try to finish my alg with those as near to solved as possible.
Once those are in place, it's just an M slice edges alg finish.
Rarely do I start a solve and not switch methods at least once during it.