I suppose you haven't been able to travel yet, due to COVID. So hope I'm not too late. But for when you eventually make the trip, there's a question to ask.
There are no limited express trains on the San'yo Main Line west of Okayama, and you're left with really the local trains (or express trains, which are not really so "express").
Well, in fact, as of March 2021, there aren't even any express trains west of Hiroshima, so you only have the local trains which stop at every single station. There is a limited express train from Kokura to Hakata, for the last leg of your trip, but that will shorten your trip by like 30 minutes so it doesn't really make a difference.
So, do you really want to travel on local trains? They are so slow, and often less than comfortable, and are as such not as pleasant to travel on as you might have thought. I suppose the reason that you want to take the local trains is either (1) to travel a bit slower so that you could visit the spots in between, or to (2) save money.
Now, if your answer is (1), then the Shinkansen isn't bad. Besides the fastest Nozomi and Mizuho trains, there are slower Hikari and Sakura trains, as well as Kodama and Tsubame trains which stop at every station. Then you can use local trains to complement the Shinkansen.
If your answer is (2), you might want to try the express bus instead. They are even cheaper than trains (if not using Seishun 18, which can only be used in specified periods of the year), and you can get a "night bus" which will travel at night. If you have no problems sleeping on the bus, then this would be preferable to local trains because it solves two problems at a time: it's cheap, and you also save time and lodging.
If you just want to try out the local trains, then go ahead, I guess :-) There isn't really need for a timetable anyways, since all trains are local until Kokura. And since you're always travelling on the same line (San'yo Main Line), all you really have to make sure is that you're travelling on the right direction, but I hope that wouldn't be too hard.