How can a lay person approach the learning process of Buddhism? I've read many books on Buddhism in the last 3 years and I started to meditate daily 10 months ago. I have a general idea about many topics, without a deep understanding of any of it. Is there a specific way in which a lay person with a deep commitment for Buddhism should approach the teachings? Is there a specific order of the subjects? Can you, please, give me some advice about where to start and how to proceed? Thank you!
There are many specific ways, giving you the best way requires a scientific study done on every possible way buddism can be taught and then finding a distinct right answer from that, which is currently, and probably never be available. I will give you a source that teaches you in a very specific and effect way of practicing buddism:

https://www.youtube.com/user/ActualizedOrg/videos

Specifically his meditation videos guide you through to enlightenment very effectively.