As you can see from my latest solve (sub 60...YES!), orient last layer is where I'm losing the most time, so, this is the order in which I memorized the algorithms:

The basics:
1: adjacent corner swap (ignoring orientation)
2: diagonal corner swap (ignoring orientation)
2.5: 3-corner orientation (maintains permutation)
3: 3-way permutation of edges (ignoring edge orientation, maintaining corner orientation)
4: 2-edge orientation

Fidrich algs:
1: 3-way edge permutation (maintains orientation)
2: 4-way edge permutation (horizontal and vertical, maintaining orientation)
3: 4-way edge permutation (diagonal)
4: Orient all corners (maintaining permutation).
5: Orient three corners (maintaining permutation).

With the eventual goal breaking the last layer into two sets of algorithms, which should I go for next?

I was thinking 3-way corner permutation (CW and CCW). Any other thoughts?

start learning some OLL's and all of the PLL's. you can then do a modified 3 step last layer. then after some time progress to a 2 step last layer. i heard that Brittany Dzoan doesnt know all of her OLL's and she is 16 sec average

You might look at CLL ELL for the Last Layer, too. Learn the hardest algs first.

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Here is what I recommend:

OLL:
2 algs for edges: F R U R' U' F' and f R U R' U' f'
7 algs for oriening corners (preserving edge orientation): look them up on any website that has a list of OLL algs

PLL: first just memorize the edge-only and corner-only cycles (5 algs), then slowly progress to memorizing all 21 PLL algs

Once you have this 3 step LL down quite nicely, progress to learning the rest of the OLL. That's my plan. I just finished figuring the best PLL algs and memorizing them, so I just practicing for a while right now, then I'll learn the rest of OLL (i know like 15-20 right now).

I'm memorizing the PLL first before the OLL. Is it better to learn the OLL before the PLL?

I think that a full PLL, is probably better than a full OLL. I only have learnt 7 OLL's, from a cross. I'm now learning all the PLL's,a dn then slowy im going to learn more and more OLL's.

PLL is a lot less algorithms, and it's also more useful (if you decide to try Petrus, for example, you can reuse it, and it's also good for blindfold cubing). If you want, you can start with a 2-look OLL (one of 3 algs for edges, then one of 5 algs for corners) and 1-look PLL (all algorithms), then go on to full OLL when you learn the rest of it.

OLL is useless without some PLLs.
Aslong as you can find a way to do OLL, (cross forming/sunes I recommend), PLL is the best to learn first.

Regarding Last Layer---

http://www.freewebs.com/cubesolution

I updated alot of crap recently as well as COLL cases WITHOUT disturbing edges.

Easy oll and easy pll page might help some people around here. Finishing F2L page has neat CE tricks for petrus users at the bottom.Correcting mistakes page is useful for everyone.The entire website is made for beginners (made this like 2 years ago for a friend) so skip all the noob chat i put in there if you will.

^_^ Have fun.