I also like to run and I've picked it up several years ago. When I'm running purely for fun, I bring my iPhone and when it's a race, i bring my small iPod mini so as to not interfere with me. I attach my iPhone in an armband on my left arm. Worried at first but it's pretty secure. Also, one thing about running with earphones is the wires. With the armband on your side, you can easily put it behind your ears since it's long enough, but anywhere else it has to go in front (usual way). This can get really annoying and distract you, I promise.
I put my keys/ID/cash inner short pocket that keeps it secure. I don't think that's big enough to hold the iPhone. Also, use a tracking system for your run, it'll be fun. I use Nike and it's fun to see that I've ran at least 1500 miles, graph showing my speed increase and also my lowest and fastest speed.
Running can be like crack. Those endorphins right after, that's the stuff.