Step 1: D-Block
Solve a 1x2x3 block on the D face and position it so that the R slice is free. This could also be done on the left side with the U-layer free. If you use the left side, your first two layers would be the left 2 layers.
Step 2: 2EE
Solve two adjacent E-layer edges using U, Uw, R, and possibly E moves and position them to create a 2x2x3 block or a pseudo 2x2x3. You may also influence the next step by orienting the last D-layer edge, or matching it with one of its corners. You may do this influencing during step one if you see the chance.
Step 3: D-Pair
Solve the missing D-layer edge and one of the missing D-layer corners. Keep in mind that you will want to have the still unsolved corner slot in the FRD position for orientation and permutation algorithms. Assuming you don't favor doing the BRD corner first, which you should, you have a 25% chance of having to do a y rotation to get the unsolved corner in the FRD position. Don't go out of your way too much to avoid a rotation though, because F moves are arguably worse. You can also try to avoid bad E-layer edge positions.
Step 4: EELS
Keyhole one of the missing E-layer edges in using ELS to orient top layer edges. You count the last E-layer edge as good or bad depending on the one in its place or depending on if you have an even/odd number of bad/good edges. This step uses 21 algs (8 mirrors). Some of these can be done intuitively.
You may run into some situations that you cannot simply do an ELS algorithm. This is either because both E-layer edges are oriented incorrectly in their correct position, or the 2 unsolved E-layer edges are in each others correct positions. If you run into the first case, just orient as many of the edges as you can while solving one of the E-layer edges and use one of 3 (1 of this will be your ELS algorithm for that case) algorithms in step 5 that deal with this situation. If you end up with the second case, you can simply move one of the edges into the top layer and influence the ELS case you'll get afterwards, or you can use an algorithm for that specific case which is included in the Extra algorithms listed with the ELS algorithms.
Step 5: LEEP
Keyhole in the last E-layer edge and phase the U-layer edges (make opposite edges opposite of each other). This step takes 9 (3 mirrors) algorithms. 6 are used when the edge is in the top layer, 1 is used when the last E-edge is solved, and the 3 mentioned in step 4 also must be counted (Remember that one of these will be your ELS alg for that case). All of these can be done intuitively except for the 3 mentioned in step 4.
Step 6: O5C
Orient the last 5 corners. This step can be recognized by the orientation of the top 4 corners (looking at the bottom corner isn't necessary), but there are some cases where you have to look at the left or back side of the cube. If you do look at the corner in the slot only for these cases, looking at the left or back side is never necessary. This step takes 23 algs. 7 are OCLLs and it takes 8 more algs and their mirrors.
Step 7: PLL+C
Place the D layer corner and permute the top layer. This takes 33 algorithms. 9 are PLLs (2 mirrors), and 24 (6 mirrors.) are without the last D corner in place.
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I chose to build the F2L this way because it saves moves, yet still sustains good look ahead and a decent move-set. You may build the F2L minus one slot with edges oriented any way you want, but this is what I think the most efficient way is for speed (balancing move count with TPS). You can solve the 1x2x3 block on the left to do an easier x rotation instead of a y rotation after step 3, but the transition to the last layer requires rotation(s) unless you learn the algorithms from this angle.
With all other speedsolving methods I know of, cubers learn extra algorithms to help out in certain cases. I have generated what I believe are the most useful extra algorithms to learn. With this method, it would be recommended, but not necessary, to learn 17 (4 mirrors) extra algorithms. 8 (1 mirror) of these algorithms orient the top layer edges while phasing just in case you end up with your edges already solved in the E layer. You should already know 3 of the 8 if you know ELS. 6 (there are 12 cases, but 6 of them are not worth it) of the algorithms orient the edges while swapping one of the E layer edges to the other remaining E slot. Note that you may end up with the last E-layer edge being placed misoriented, but you should already know algorithms for this from step 5. The last 6 (3 mirrors) algorithms place the last E edge while phasing and preserving the orientation of the comers in case they end up oriented.
Pros - Low average movecount for a speedsolving method. No large algorithm sets. Can be broken down easily making it suitable for beginners to learn.
Cons - Uses F moves in the F2L. Occasionally requires a rotation.