Jeremy- I print out a huge fretboard diagram on legal paper- use landscape mode. I use one that has the notes included, then I circle the I IV V or whichever progression is being played. As Tomo said, I try my best to target those notes the best I can when the chord changes respectively. Pay attention to the pattern of the I IV V as it will repeat on the fretboard. It definitely adds depth to my playing and sounds more melodic vs. playing all the notes in the scale just hoping to hit on a tonal center. It's often more about the notes you do not play than the ones you do. I think Tomo leans away from diagrams- he's probably right but it really helps me to see it in addition to his ear training which is key. It's a great combination for me.
Further, I highlight with a marker all the notes in the scale (the pattern) and circle in RED the exact notes e.g., for Em Blues, I would circle in red E(I), A(IV), B(V). I start with blues because you can find plenty of slow backing tracks to practice to and the progression and turn around are easy to pick out. Like Tomo said, you have to develop your ear first so you are not memorizing, but actually learning. For me, a goal is to be able to play with my eye closed. That said, there really are no rules in Rock n' Roll so do what sounds good to you (and maybe others!) Also, don't get too worried about perfect scales and tonal centers as tonal centers, at least to some degree can be subjective and are not 100% independent from what you are playing. It will all makes sense in time- music is like art. It's not perfect (is not meant to be) and it's never done (hopefully.)