I don't think you need to do any more than a couple minutes fast walk/very slow jog to warm up.
Well done on "nearly" enjoying your last run. The key to sticking to it is to enjoy it : let's face it, if you run eyeballs out every time, you won't enjoy it, and after a few weeks decide this is not for you. Given a choice, no-one carries on doing stuff they don't enjoy. So take it slow, look at the scenery, and forget your watch.
I don't know what your own goals are, but I started running in order to run a marathon. I spent the first 3 months focusing solely on time on my feet rather than speed/distance. It is only once I could comfortably run for 2 hours that I started to inject some speedwork into my training. I suggest (once again not knowing what your goals are) that you should not even think about speed until you can run comfortably for 30 minutes+. One way to achieve this is to get a heart rate monitor and keep your heart rate below 75% max HR.
Hope this helps, enjoy your running.
Oh, and with regard to your knee, make sure you stretch every major muscle group after every run (calves, lower calves, quads, hamstrings, glutes/piriformis).