Yes, I think that you're off to a good start.
Hey, I started running 2.5 years ago when I was 27. I did about 8 weeks of training similar to what you described (3-4 miles runs all at a moderate/challenging pace for me) to prepare for a local 5K that my company decided to enter a team into. I ran 22:45 and decided I wanted to improve upon that. I've gone from 235 pounds to 175 and have dropped the 5K to 17:36. I still want to get much faster, but I'm realistic about my personal time constraints and other obligations. Heck, I won my first race a couple of weeks ago with that 17:36! What a feeling that was for someone who didn't run a couple of years ago!
So my point is that I can relate to you, and although most of the people on here would say I'm so slow I should shoot myself in the neck with a cross bow and do the running community a favor, I'm pleased with the progress I've made in the last couple of years. As others have said, you must be somewhat athletic and in respectable shape.
For me, I think the improvements have come through a weekly long run, a good tempo run each week, and making sure I run EASY on my easy days. Find a local group to run with. I've found it to be very helpful.