Progress report:
After almost 4 weeks of cubing I'm consistently solving around 1:30 with the beginner method. I'm now learning 2 look OLL and 2 look PLL. Good news: When I remember my algs correctly my times are dropping down to the 1:10 range. When I don't remember my algs correctly I get a complete train wreck

I practice and practice the algs, but when the timer starts I'm somehow missing a move and end up with a white face on the top. Oh well, that's nothing that more practice can't fix.
My goal a week ago was to have a sub 1:30 Ao5 and I've hit that several times. A 1 minute average seems far away, but then again, a sub 2 minute average seemed impossible 4 weeks ago.
Even though I'm focusing on learning my OLL and PLL algs I'm finding that just by solving a couple hundred times I'm getting faster and faster with the white cross. I'm rarely solving the cross in place but I'm now solving the cross in the proper color relationship to each other and then rotating into place. It's interesting to see the change in my perception of the cube. This thing was a total mystery a month ago and each day it's making more and more sense. I'm really enjoying that part of the process.