I had "issues" with muscle spasms, burning, and tightening up when first started walking, too. I was very heavy and I'd been sedentary for a long time. Most of the time I could walk through it, but there were times when I had to stop and stretch. These problems didn't last long. Within a few weeks my body stopped complaining and I was increasing my speed and distance almost everyday. It doesn't take much regular activity before you start getting more fit.

4 MPH is a really fast walk. Initially I walked only 2.5 mph. These days I walk between 3 and 3.5 mph. I never really enjoyed speed walking. I wanted to enjoy myself. So I just tried to find the right balance between casual walking and walking like I was going somewhere. What I found most beneficial was workout time (and yes, for me walking is a workout). If my workout was less than 30 minutes I didn't even feel warmed up. If I got in at least 30 minutes I'd get that pleasant endorphin buzz and general feeling of well-being after a walk. That effect became something that I'd look forward to. Soon a 2 or 3 days per week walking routine turned into an everyday habit. I enjoy my walks and I don't feel that the day is complete unless I've gotten out and moved.

I'm glad that you are past the pain part of it. Let the fun begin.