Ok, my advice is that for corners first, you actually don't do the corners first. To succeed with corners first, the MOST important thing to be good at is the First layer (minus one edge for most methods). If you are wanting to be very good, then the order I recommend is:
1) Solve 1 layer (or minus 1 edge) in any way you want (to average less than 20 seconds, this step should take less than 10 seconds). There are pretty much 3 ways you can solve the first layer. The first way is to solve the corners first, then the edges and the center. The advantage of this is that you always need less than 20 moves, and the recognition is very good. The second way is to solve a cross, then solve the corners. The recognition is good for this way, but it can take more than 20 moves. The third way is block-building. This way is very good if you want to use as few moves as possible, but it takes a better recognition. If you use this method for the first layer, then you have to do a lot of work, and you must understand how a rubik's cube works very well.
2) Solve the Corners. The best way to do this is in one algorithm, and learn the recognition described on Waterman's website. This takes a lot of work, and many algorithms. If you don't want to learn so many algorithms, then you can orient the corners first, then permute them. The other option is permute then orient.
3) Solve the rest of the cube however you normally would. This should take very little time, because the turns are all URM moves, and recognition is very good.
The reason I am telling you that this is a better way to solve it is because of recognition. Solving the corners first, then solving the edges does not set you up very well for the later steps.
You do not have to learn all the algorithms in the Waterman method to be a good corners first user, but you have to be very good at doing the first steps. I hope this makes sense/helped in any way.
If you are planning to learn all of Waterman, then I'd say you should learn only the algorithms you require first, then gradually learn the others.