I agree with the previous posters, you don’t need to go into the mythology at all. In fact, the mythology doesn’t really deal runes in a direct way, they are mentioned, but not necessarily what they are or how to use them. Like @FraterMagni, I’m a culture geek, so I like the connection.
As @runeskribe says, the gods do have a strong connection with the runes, but you don’t have to know that to divine with them.
My suggestion would be to read the rune poems as if each rune has two or three verses. Then meditate on the rune (and it doesn’t have to be very long, a half an hour meditation works to get you started) and then you’ll have a meaning that you can work with. The runes, as a force, are pretty open to wanting you to understand them.
Now, the supercool thing about the runes are all the layers to them. At first, they seem like this simple divination technique (fehu means money, uruz means untameable strength, thurisaz means bad stuff, etc). But as you study them, you find that many are Aesir, many of jotuns, many are Powers that are more chthonic. It’s layers are what them fascinating, and one could study them for a lifetime.