I wouldn't necessarily start learning all the "rules of thumb" stuff like the Sunny 16 rule. Don't get me wrong, they are useful, but it might muddy things up for you.
You are almost there. You need to decouple yourself from the camera's meter a little more. Yes, you can use the "middle" as a guide, but as already mentioned, understand that the meter can be easily fooled and you have to give the scene some thought and make adjustments accordingly.
Soon enough, you will begin to realize that certain situations will require certain adjustments. OK, snow, overexpose by at least a stop and a half, maybe even more. OK, shooting into the sun. I need to expose for the sky and use fill flash for the subject, etc, etc.
Yes, check your histogram, but don't be afraid of a little bit of clipping. You will learn that you can blow out the sky a little bit and still recover in post. If you aren't doing so already, shoot in RAW. What you see on your histogram will vary greatly based on what you are shooting. So just make sure you have good amount of information registered in the histogram and you should be fine.

