Interesting inputs: I don’t feel the same at all. For example, I never understood the “lose 50 or 100 games as quickly as possible” thing: I played maybe only 25 games (on 19x19), including only 5 games with real people (instead of programs), and am probably close to 8 kyu OGS (correspondence games). So let me chime in. The following applies at least to making progress in slow (correspondence) games.
I strongly believe in the following principle, for making fast progress: play against players who are at about your level, so that you can have a chance at both winning and losing, and so that you can understand your opponent’s moves. Some programs automatically provide this for you (Igowin iOS, SmartGo iOS,…). Similarly, I almost never look at pro games (and I am not completely alone in doing this ): behind each move hides a mountain of reasons that cannot be climbed unless you reach a very high level (dan and more, I guess).
Another principle: many important things can be practiced on a 9x9 board (life and death, counting,…), so I would definitely start with that. More things can be practiced on 13x13 (influence,…), so I’d continue with that. Then 19x19. A program like SmartGo Kifu automatically moves you through these steps. In order to make progress, review your games move by move and find out why you lost (or won).
Another principle: there is a lot of wisdom in books, and it can be best appreciated when you always guess the next move on diagrams, as this both gives practice and let’s you explore the reasons behind each move. SmartGo Books allows you to do this. As for the subjects, it seems quite logical to me to start with basic bricks first: the opening is the basis for a whole game, shape and tesujis are the basis for longer sequences.
Yet another principle: doing exercises is like playing many small game bits, and this is best done by reading a good part of move tree (before checking the solution), and when the correction explains why some moves don’t work, as this many not always be obvious. Again, this allows one to explore the reasons behind moves. Life and death problems are particularly interesting for practicing the very important skill of reading, because a small mistake can be fatal, so they encourage accurate reading, which is a crucial skill. Otherwise kinds of problems are precious too: for example, opening problems allow you to practice opening principles without having to play many, many games. SmartGo Kifu has many such exercises, and there are many others on the web.
Also: practicing with programs is good, but you learn to beat their strengths, not their weaknesses: a variety of opponents is important, and this great variety is found in playing with real people.
A recurring theme in the points above is the idea that a deliberate pondering and a slow but deep exploration can teach a lot, in go.