Congrats Personally I have found that when I go for a run it improves my mood a lot more than when I don't exercise. I even had a Dr tell me that exercise is often more effective than taking mild anti-depressents.
Re - getting into running. The best thing to do is a 5k plan - I did one that was called podrunner intervals which was an 8 week walk/run plan to 5k. By the end of it I was able to run the full 5k and have never looked back! As an added incentive, why don't you enter yourself into a 5k run which is at the end of the plan - that gives you something to work towards.
While I wouldn't say that I take part in an event purely for a medal, I do still treasure all of mine. I got a medal for the first 'official' run which I took part in - it was only a 5k but I was inordinately proud of that medal as to me 5k had seemed like a huge achievement. Now I have a full marathon medal and am ridiculously proud of that. I look upon the medals I now have with pride and they all have sentimental value - but maybe I'm just a bit too sentimental!
If medals were only given out to those who got below a certain time then that would very unfair to all those who trained very hard and didn't get below a certain time. I would have been very disappointed if I had not got a medal for my marathon purely because I had taken longer than 4 hours to run it. Shallow maybe, but I am pleased to have a memento to remember the occasion by!
One other thing I really liked in the Amsterdam marathon was the App so people could track you on the course. Not sure if other marathon's also do it but it worked really well - my OH downloaded it and was able to track me on the course and figure out when he needed to get out of bed to cheer me over the finish line.