Is it better to post my efforts from the lessons, in the Drawing lesson forum, or just stick to putting them in the Gallery?

It depends what kind of response you are expecting. Personally I always posted my lesson exercises in a specific album for this purpose in the gallery since my intention was merely to have a record of my progress. But there is no reason why you should not post your drawings also in General discussion. If you are looking for comments and critique the General Discussion forum is your best option since you are unlikely to get any response at all in the lesson forum.