Sorry about the late posts, but I was in Edinburgh with no access to a computer.
To my mind there are three main ways of learning a language.
1 - You teach yourself the language using books, CDs etc.
2 - Lessons make up the bulk of your learning, with vocab and grammar drills outside of class to reinforce what you have learnt.
3 - Mainly self study, but with the biweekly or monthly lesson to clear up misconceptions, correct pronunciation, and generally just push you in the right direction.
Now, which method is best for you relies mainly on just one thing. Can you teach yourself a language? If the answer is yes, then you should probably choose method number 1.
If the answer is kind of, then choose option number 3. And, if the answer is no, then clearly option number 2 is your best choice.
But, it isn't that simple. There are some major differences between self-study and lessons.
Self-study is potentially much faster than lessons. You can self-study for 8 hours a day if you wanted to, whereas 8 hours of lessons a day would be very expensive.
Lessons are generally slower overall than self-study, but they are more structured and thought out.
Think of self-study as a man who is skiing down a mountain, and someone who takes regular language lessons as someone taking a ski-lift down the mountain.
If you are a good skier then you will easily beat the ski-lift to the bottom of the mountain. But, if you are a beginner then the stopping and starting will mean that the ski-lift will easily beat you to the bottom.
If you are the man on the ski-lift then you will make slow and steady progress. Regardless of what happens, everyday you will get closer to the bottom of that mountain.
So that's my butchered metaphor.
There is also the cost. Self-study is undoubtedly cheaper. Books cost £20. Internet resources are free. Private lessons cost about £20 an hour. Weekly evening courses are about £250 for a year. There is really no comparison. Self-study is always cheaper.
So there are all the factors I think that matter. It leads me to this conclusion.
Personally, to learn a European language I don't mind self-studying. But, for difficult languages like Arabic or Mandarin I need lessons. I need a teacher explaining the finer points of grammar, and teaching me pronunciation. So for example, if I wanted to learn Italian (the next language on my European language list) I would get on Memrise, Duolingo, maybe buy a grammar book, and if things got difficult I would get a few lessons to clear things up and put me back on track.
However, if I was learning Cantonese I would be looking at lessons and courses, because if I was self-studying Cantonese I would get bogged down in its alien complexity, and it would take me years to learn. With regular lessons, I feel confident I could learn it in less than 18 months.