Your best bet is to pay an expert consultant.

Beyond that: it first of all depends on how in-depth you want to go with each article or video. If you just want to, say, rehearse the fact of Tokugawa's life, you can probably do a pretty good job with Wikipedia (I know, I know) and something like the Cambridge History/New History of ____ series. It'll be dry, but it'll have the facts.

If you want to get more at a historical argument question, like you suggested with "why Nobunaga mattered," approach it like an undergrad paper! No need to spend years of research! Find a couple of relatively recently published books from university presses or other reputable academic ones (look at the bibliography of a good recent Asian history book. You'll see what publishers show up over and over). Build your bibliography from there; approach the article or video like you would a paper (argument, evidence).

If you want to do a Cool Stuff About -type video or article, I would definitely recommend making sure that all of your facts are either cited to a primary source, or are found in at least two secondary works that are not citing the same (non primary) source.

Cool project!

I recommend getting a membership for your State (or equivalent) or National Library. This should give you access to a lot of digitalised past and current issues of academic journals, as well as some online access to books. The journal access is the most important, though, since it should allow you to find review articles for any book you're interested in reading. If there's not a review (i.e. if it's a particularly bad pop-history book or an old work that didn't make many waves at the time), that's usually a good indication that you should avoid that book.

Reviews are also an important way of understanding the flaws in a work - sometimes alternatives that offer better coverage of the weaker parts of the book are provided - and also help you identify different schools of thought. For example, if you wanted to learn about warfare in the Early Middle Ages, you might come across Guy Halsall's Warfare and Society in the Barbarian West, 450-900, which serves as the most modern synthesis on the topic. Looking into the reviews, you'll find that they're overwhelming positive, though reading multiple reviews will highlight a number of flaws. Nicholas Brooks, for instance, points out some minor weaknesses in Halsall's understanding of the Anglo-Saxon world, as well as the weakness of his arguments for Anglo-Saxon use of cavalry. Meanwhile, Eric J. Goldberg notes that Halsall doesn't make sufficient use of royal diplomas and monastic charters when discussing military organisation and logistics and also that he hasn't paid sufficient attention to recent archaeology of Slavic fortified centers, which demonstrate just how powerful the Slavic rulers the Franks were facing could be.

Bernard Bachrach, on the other hand, is very vocal in his opinion that Halsall is a hack and a terrible scholar. This is where you should start to realise that there are two, very different, views of warfare in the Early Middle Ages, and that you've just found the other side. A quick search of reviews of Bernard Bachrach's work will turn up a review by Guy Halsall of Bacharach's Early Carolingian Warfare, wherein he airs his own grievances with Bachrach.

Having read these reviews, you now know a couple of things. Firstly, a significant number of scholars, including specialists, consider Halsall reliable, if not perfect. Secondly, there's an alternate view of Early Medieval warfare, and a lot of it comes down to interpretation of sources. From here, you're going to need to read both Guy Halsall and Bernard Bachrach and try to get a feel for what each is saying (and don't pay too much attention to what each claims the other is saying or is saying about them - scholars are often no better than random people on the internet at fully representing their opponent's arguments). You'll also need to do more research on what the world outside of warfare was like. Searching your State/National library for books on the Early Middle Ages will almost certainly turn up something like Chris Wickham's The Inheritance of Rome or the relevant volumes of The New Cambridge Medieval History, which reviews will tell you are solid works. Goldberg's mention of recent archaeological work on the Slavic settlements also suggests an avenue you should take. Another search will reveal Florin Curtin's The Making of the Slavs and Southeastern Europe in the Middle Ages, 500–1250 to be two books that deal with this area.

(Obviously I've cut out the step of going through multiple reviews for the supplementary texts, but they need to be examined in the same way as the initial text. I should also mention that you should look for recent books, articles, etc whenever possible. Some very specific monographs or journal articles hold up very well even decades later and don't need much reinterpretation, but it's hard to know which these are, and so sticking to more recent works (I recommend published within 30 years or less as a rule of thumb) is generally better practice.)

Searching the library catalogue will also help you find journal articles about specific topics or subjects. You can do a search for blanket terms (like "Anglo-Saxon cavalry", for example), or look through the bibliography and citations of the books you've selected for titles that seem relevant to your interest or which are referenced for a specific topic you'd like to know more about.

Once you have a better understanding of the period and have read some additional work on areas that one or the other are weak on, you can begin to make your own judgements about whether you want to follow Halsall or Bachrach's interpretation and what modifications you think need to be made. This, mind, won't necessarily be a very informed decision - you'd need to be an actual expert to truly make an informed choice (I know I can't) - but it will allow you to discuss alternative viewpoints and why you - or the other author - believe this is wrong.

I've used a specific topic and authors as an example here, but it can be generally applied to pretty much anything. Find what looks to be a good general introduction to the subject, read the academic reviews to determine if it is useful and to see if there are alternate viewpoints, then dig a bit deeper looking for more information on areas that reviewers have highlighted as being weak in the work and read the counter arguments of scholars who have a different approach to the topic. This doesn't guarantee that you won't end up on /r/badhistory, but it will greatly reduce the chances.

Building off both /u/sunagainstgold and /u/hergrim you may want to, as a starting point, resign yourself to the point that short of paying an expert to look at it, or spending a year or so studying that particular topic, there probably will be parts of it that specialists will quibble with or even strongly object to. If not a specialist on that particular topic, then a specialist on some general topic (say, military history) represented or used as a basis for an argument in your work.

As a non-historian who has gained my knowledge through "hobbyist studies" I think about this a lot. It seems like every time I go back to re-read a secondary source, I read it a bit differently and come away with a different take on it. In my particular case, there's an unlucky lack of overlap - works on Persian history tend to be useless as sources on Persian religion, and vice versa. But the things that may make me and others consider a source like Zoroastrians: Their Religious Beliefs and Practices to be a grossly misleading guide to the Achaemenid Empire, for example that Darius' story of the "False Bardiya" should be taken seriously, may be (and is) happily cited by specialists in, say, Jewish and Christian history. If I read a better source like Pierre Briant's From Cyrus to Alexander, I might get a better picture of that, but come away with the understanding that nomadic societies are necessarily poorly socially organized, since he uses this as the basis of a particular argument. Those who study the civilizations of the Eurasian steppe would probably do a spit take at that reasoning.

It's never possible to gain a specialist's understanding of every single topic, of course, so these issues are simple facts of life. But one concrete recommendation I would make to mitigate these problems is to set some constraints (region, subject, era, etc) on the topics you approach. That will allow you to build a broader understanding and recognize when an author may be on thin ice (e.g., you'll notice when they stray outside what the source material tells us). If you do a Dan Carlin-style "Big Things In World History" thing... you probably won't.

I'm mostly repeating things that have already been said, but I thought you might like the perspective of someone who hasn't studied history at university level.

What sort of topics are you interested in? That may go some way in helping you find the lay of the land and avoid obvious pitfalls.