Hanson's block diagram is a very good place to start - as you've noticed, there's a lot of detail there, in the signal names and their use within the datapath.
The signal names in visual6502 are in many cases inherited from the block diagram, which should help you piece together the way things work.
The use of both clock phases allows the 6502 to make very efficient use of time: three cycles is really four in many cases, because of overlap between consecutive instructions, and four cycles is really eight phases, which might or might not be helpful way to look at things.
You can trace the registers, latches, internal data busses and the datapath control signals, and show behaviour phase by phase, in visual6502. And I think that's worth doing. As with the block diagram, there's lots to study in the tabulation you get.
It might be worth trying to get an independent understanding of a datapath before tackling the very specific 6502. It's possible the nand2tetris book/website/course would be a good way to do that. For myself, I think I learned a lot from Tanenbaum's book, _Structured Computer Organisation_
I'd say visual6502 is a very useful tool, and that there's no need to feel you have to understand the transistor level. It's enough to have a good picture of the datapath, and then to run a simulation like this:
http://visual6502.org/JSSim/expert.html ... ,DPControlYou can then see exactly what's happening in the datapath, and what the datapath control signals are doing.
If you want to run specific instructions, you can do it like this:
http://visual6502.org/JSSim/expert.html ... 056908eaea