As for the rest of the responses, it seems like there is no general consensus on what direction to go in, but a lot of the responses gear towards learning some type of PLL/OLL.
That's mostly because something like 80-90% of the cubing community uses some form of CFOP (cross, f2l, oll, pll) to speedsolve, and the world record as well as the vast majority of the top 100 averages are with CFOP. Whether that's because CFOP is a better method or just because more people use it is anyone's guess (I tend towards the latter viewpoint).
There are at least several people averaging sub-20 with the Roux and Petrus methods as well, however, and both of these methods have lower average move counts than CFOP. It's just that more people happen to use CFOP (probably both for historical reasons and because it involves less thinking to learn), so you are more likely to get help from people online with CFOP questions (although I'm sure someone like Kirjava could answer any Roux questions you have). You should definitely look into both Petrus and Roux and see if you like either approach better than LBL (layer by layer) methods.
If I'm not mistaken, I think the fish is the same thing as the sune? So I need to just sack up and learn those alg's. But it seems like a 2-look PLL or something along those lines is what I should get into next?
I've never heard of the word "fish" being used to refer to a particular algorithm (I looked it up on the speedsolving wiki and apparently it refers to an OLL case type, but I've never heard it before on the forum). Sune is always used to refer to the algorithm R U R' U R U2 R', which can be used alongside F R U R' U' F' for a basic 2-algorithm OLL method.
Yeah, if you want to get fast at any LBL method you pretty much have to memorize the 14 algorithms for 4LLL as a bear minimum.
You can start with just learning 3 algs for a beginner's OLL/PLL last layer method (see
http://badmephisto.com/begsoln/) if you don't already know them. Later you can add 4 more algs for 2-look PLL, then later the last 7 for 2-look OLL.