What are your favourite way to learn BH corners? Just scrambling a cube and trying to solve corners (of course after understanding method) or comparing your solutions to optimized algs from BH website, doing it from the beginning to the end of the list?
For me it was essentially your second suggestion. I liked going through the algorithms alphabetically (according to the way I've chosen to letter the pieces in pairs), trying to figure out a solution for each one, and then comparing the move count with the count at the BH website. I almost never bothered to even look at the algorithms at the website - I only bothered if my solution seemed particularly ugly and I was hoping for better. Since I have letter pairs for each case, and my buffer piece was "A" (so I never had a letter pair that started with "A"), I would just start with "BC" and try to solve it, then "BD", etc. After each one, I'd invert it, so that I could still work from a solved cube. So I'd do "BC", then "CB", then "BD", then "DB", then "BE", then "EB", etc. I would do all the "B"s that way, then run through them again, until I had gone through all 18 of those a few times (maybe 5 to 10 times). Then I'd start with "CD" and go from there. With "CD", now you only need 17 cases (since you already did "CB" as the inverse of "BC"), so each group is shorter to learn than the previous one.
I liked to do time attacks on each starting letter. That way you'd learn to get fast at it. I was doing time attacks when I had only practiced the first few letters worth.
It only took me a few weeks to get halfway decent at BH corners this way. And it was fun, because it was constantly just trying to solve a puzzle each time, until they got easy, whereupon it was more like doing PLL time attacks.
Other people I know didn't learn them that way - they preferred to learn them by class. But I really like how my approach worked out. I'm really fast with corners. My edges aren't as fast, and I suspect that's partly because I didn't learn them this way. I think the time attacks can really help.