TwisterTimmy, God of Rubic 2, MarcelP:
As regards the best place to get started with full OLL/PLL, some of badmephistos algs are a bit out of date, and have essentially been replaced (in top cubers repertoires) by algs requiring fewer regrips, or that are more fingertrickable. As a for example, the E perm given is not used by anyone really fast anymore, the N perms are out of fashion etc etc. I keep detailed records of the alg sets used by many of the top cubers, so I am offering these two documents as a starting point. All the algs contained herein are sub 1-able, and are in the order I learned them in.
This list is optimised for the right hand heavy cuber, I would make different suggestions for the more ambidextrous or hand balanced cuber, and there are a couple of instances where the choice is one that makes sense fingertrick wise for the 4-look cuber, but you may wish to replace with a more difficult to learn alg that requires fewer regrips in future.
The major areas of debate around which PLL algs are good include:
1) U-perms (many prefer more optimal M move algs),
2) whether the U moves in H and Z perms are U or U' (basically depends on how you execute M'/M2 moves),
3) Robert Yau has put forward some very useable alternative V perms,
4) there is a lot of debate about N perms (Na alternatives include RUR’U then Jb perm, Nb there is a good RUF alternative),
5) there is a good bar left F perm using RUF,
6) there is a favourable Ra which is simply the mirror of Rb on the left. Right hand heavy cubers find it more difficult,
7) and for Ja there is a very fingertrickable bar at left version.
As for OLL, the only ones I would really considering changing from this list are:
OLL 3, 4 and 17, there are regripless M slice versions out there, but those given are easier to learn since they are simple f2l extraction/insertions
OLL 43, 47, there are potentially better algs if you are left hand heavy/balanced
OLL 39, there are alternatives if you are really bad with the left hand
OLL 37 is a bit idiosyncratic, but it makes sense to my muscle memory
I fully expect many would disagree with my some of my choices, but after considerable research, these are in my opinion the best place to start, and then if there are any you really don't get on with, then check out the alternatives on the wiki, or watch some ninja cubers on youtube and copy their algs. I would suggest not bothering with an alg unless you have seen it executed sub-1, as these guys are doing the leg work to find the absolute best possible algs so you don't have to! It also reduces the contenders for a given alg from 20-30 on the wiki, to 3 or 4 that you know definitely have potential.
I would also, as you get more advanced, consider learning some algs that can be executed from different angles to those given, to avoid AUF.
The main ones that people learn extra for are Ua and Ub (bar front).
There are also good algs for Aa and Ab (solved corner top left), Vs (with corner top right), 180 degree T-perms and different perm endings to avoid post PLL AUF, F with bar left and/or toward, Ja (bar left or right), Jb (bar right), G perms (headlight toward), and a Gc (headlights right).
However, all told, if you learn the Ua and Ub alternatives, you don't really need to worry until you are sub-10!