reliable enough for quick answers

If you're looking for quick answers in history, you may have some pretty severe difficulties. If you want to know the wingspan of a B-29 you may be in luck, and other simple facts are somewhat readily available. Other simple facts can be maddeningly difficult to get your hands on. In a recent friendly debate on this subreddit on the subject of the Battle of Britain, I once again came up empty on one set of facts that would have helped my argument. I can cite fighter production statistics by month during the battle. Similarly, I can quote casualties broken down by month, week, or even daily. What I can't find is how many pilots were available over any time period during the battle other than at the very beginning and at the very end. It's a simple fact, but I can't find it.

History is like that sometimes. It can be maddening, but when you find that elusive fact that you have been hunting it can be glorious as well.

Now we can address another of your statements:

However, with history, there is often a lot of speculation (perhaps I ought to say, it's possible to find a wide range of opinion)

Once you go beyond the bare facts, this is what history is. My specialization here--Pius XII during WWII--has no one book on the subject that I feel is adequate. There are a dozen or more books that might be in your local library that discuss the subject, but none of them will cover the range of facts and opinions on Pius XII's role during WWII. My own post on the subject hit the character limit...three times. Even simpler subjects--was the Sherman tank a success or a failure--can't be answered in a sentence and probably cannot be adequately addressed in anything less than two good paragraphs.

How on earth can a layperson research historical questions reliably?

Your main tool is to not trust any one source. If you have an interest in a subject--not just a brief spark where you go to wikipedia and find an unreliable answer but a real interest--read two or more sources on the topic. This is how you begin to protect yourself from the bias or quality of any one source and begin to gain a base of knowledge. The items that are the same in the two sources are indications that they can be trusted a bit more than those items that disagree. Get to six or seven sources on the subject and you have a real good chance that any disagreements among historians will have come to light.

Any one source is suspect. If you have to only use one source, finding a historian that has published a number of books on the topic will give you the assurance that people have found his or her works worth investing in monetarily. The author could still be highly biased or even completely discredited, but they had some money behind them at one point.

Even here, any one poster will have bias and limits on their knowledge. If you want something other than the "quick answers" available on wikipedia and the like, then you are likely going to have to put in the effort to be an amateur historian.

I hope the above helps!