This is inside baseball, folks, so your mileage may vary.
Whatever lectionary (sequence of readings for Sundays) you use, you’ll end up with three readings and propers (introit, gradual, etc) for the Sunday. Often they work together, with a common theme bridging all the propers together. This is very common in the One Year lectionary, especially with the collect, introit and Gospel.
But don’t assume they all go together the same way, or that you have to connect them. Look, especially in the Three Year lectionary, there is the feature of a lectio continua (or really a lectio semi-continua) –a series of readings from one book, not necessarily coordinated with the Gospel. And in the One Year you don’t have a one-for-one correspondence either.
When you preach, look at the propers and other texts, borrow their language on occasion, but preach the text. Don’t preach the propers. Don’t try to link it all together into some tapestry of church-stuff. Preach the text. Preach one text. Learn what it says. Meditate on it. Research, pray and ponder. Preach that one text.
Then, if you are able, if you desire, if it fits, go back and look at the other propers again and see what else there is that may connect.
You preach the text of Scripture, not the propers.