The problems are the key. In general texts are better than video since the problems are a designed part of the text. I don't know about Khan or some other tour de force video series. It is certainly possible to have a great video set with great accompanying problems. But I think much rarer.
My advice would be to go with a text. I find the ones from ~1900 to 1960 best. They are written more directly and with smaller words. They will generally have the answers (key requirement for self study). Will have a variety of problems from simple use the equation to harder. And will have sufficient volume of problems that you can do both drill and design self tests. The ideal text of course would be a programmed instruction text but this is rare.
*"Would time be better spent doing more exercises and less video lectures?"
*"Video before or after text".
In general, I would find a text that is the main thrust of your learning and not spend much time on videos unless for specific issues. (so...mostly "after").
I think systematic summarizing is overkill. Most importantly, work the example problems systematically (in same notebook as exercises as you read the text. Feel free to keep occasional notes, but don't rewrite each chapter. However, a great practice is to have section for Q&A. (end of notebook backwards works well.) Often you will find that as you work exercises or read further, you figure out the question, but for a few you may not, but then this gives you a very specific list to ask questions on SE or with a tutor or teacher or parent. (I think there will be few questions that really need to be escalated and many that you solve for yourself as you go. But just having a "parking lot" list like this keeps the mind at peace as you are learning, that you will get everythign sorted.) In any case the real proof of the pudding is in exercises and self tests, not in reading/parsing.
*"read first or do problems first?"
My advice is to read the section first. (Good books will not have long chapters, but short sections instead.) Read it fairly quickly but carefully. Sounds strange, but I mean not lackadaisically like a novel but in an engaged concentrating mode. But still with some speed. Not to skim or miss anything. But with a desire to be time efficient and get to problems. This will be a little bit of a strain until you get used it it.
After you finish the section, do the problems. Try to do this without looking at the text. Treat it as a practice test. If your book has a lot of problems, I would do the odds as first HW and save the evens for self testing as you progress (later tests for seeing if you remember.) Check your HW for answers. Any problems you missed, rework the entire problem from scratch (but not the problem set) even if it is a silly sign error or the like.