I think you're trying things the wrong way around, I'll try to explain.
Design patterns are solutions with a name for common problems. The "gang of four" design pattern book is quite literally that.
The first question you need to answer to apply any design patterns is thus, "what is my problem?", or more realistically, "how can I split my actual problem into a set of common problems?" (any real-world problem is never a single pattern).
A second thing to consider is that the world does not only have common problems, it also has non-common problems. Any real-world problem is thus not a set of common problems where you can apply design patterns, there are also bits and pieces in it that don't fit, no matter how you turn, twist, and look at it.
I believe you can only answer "which design pattern to apply" after you have made an OO design that solves your problem. At that point you understand the problem, you can see how the classes in the solution interact, and identify the patterns and the parts that don't fit.
That means in my view, you first do a proper OO design using the SOLID principles as listed in [1] so you have a good understanding of the problem you're solving, and second, find patterns.
I always skip the second step, and instead just implement the design as I found it.
Design patterns to me are useful for communication. I can say "Adapter pattern", and you and I understand what we're talking about. This beats having to make a PDF with a collection of classes and objects to explain what I mean.
A second use of design patterns to me is that they are a source of inspiration. They solve the common problems nicely, and you can apply similar tricks to solve your real-world problems.
Trying to apply a design pattern without understanding what you're solving feels to me like picking a solution and then trying to push the problem into the shape of the solution. As an extreme example, you pick a hammer and a nail to put the painting up at the wall, even though you then find the wall is made of concrete. Will you manage to put up the painting? yep, you likely can (software is extremely flexible). Is it a nice proper job? well, I have to see the result to believe it.
A simpler path to me seems to first examine the wall, and then decide about the solution. In other words, do a OO design using SOLID, before thinking in design patterns.
[1] https://en.wikipedia.org/wiki/SOLID