This is a bit of a mash up of different thoughts after my second full shave, but I'm looking for some advice as well as opinions.
I've just recently bought a set up from Straight razor designs, I just completed immediately before writing this. Things went great the first couple days, the cheeks and sideburns were pretty straight forward. Shaving my neck was fairly easy, even if it did take some interesting contortions to stay (mostly) with the grain. When I decided to go for my first full shave, and tackle the chin and upper lip, I started experiencing pulling and a lot of discomfort, through my whole shave. Thinking it was my technique, I tried again today, and started having the same issues. So, I stopped, I decided to try some of the bigellow shave cream I've had for a while, instead of the SRD soap, I had never used the cream in a mug before, and I now know why my shave wasn't going well, the "lather" I created using the soap was pitiful.

On to the advice, How should I go about getting that rich creamy lather with a soap, specifically the SRD soap?
Does quality of the water affect a soap more than a cream? I have distilled water on hand, for other reasons, should I try lathering with that?

On an unrelated topic, I currently use Clubman after shave, I have for years, but I think I want to find something that moisturizes a bit. Does any one have any suggestions? I do prefer something more classic, like clubman, but I'm open to newer stuff if it works well.