Hello,
First, congratulations on overcoming your fear of treadmill and making that first step!
Second, I'm totally jealous of you getting picked for the Parade Grand Marshall - so cool!!
Anyways, I just wanted to share my 2 cents about starting out running:
1) Totally agree with the previous advices of going slow in the beginning.
2) Totally, totally agree with listening to your body advice! and I will add that don't wait too long to get a professional advice if you are in pain! When I started running, my right knee started to hurt after I was running for 6 months or so. I asked around, was told to ice it and it should go away. Iced it, and ran again and still hurt! Went to see PT and was told my IT band is very tight and my other leg muscles were too weak (common for beginner runner). So I did certain stretches and leg strength training - helped for a while, but then it came back again! Turns out (my chiropractor who has orthopedic background found out), my right foot bone was just a little off right beneath the ankle, and the impact load I was adding from running made the IT band problem worse. I got adjusted and sicne then it's been smooth sailing

So don't be shy about asking for medical help.
3) As for C25K vs Jeff Galloway, I tried both and they are both good programs. Here's a very basic definition of the programs:
C25K: Sitting on a couch -> walking 30 minutes -> add small amount of running in 30minute walk -> increase the amount of running, decrease the walking in 30 minute -> running with no walking for 30 minutes -> running 5K (3.1 miles) with no walking
JG: Sitting on a couch-> walking 30 minutes (or so) -> add small amount of running by running 30 seconds and walking 60 seconds and repeating this for 30 minutes total (or so) -> increase the running as you become more fit but always taking walk break (such as, 1minute run/1minute walk to 2minute run/1minute walk) and repeating the cycle to your desired distance ->Whether you're doing 5K or marathon, JG method means run, walk, run, repeat till finish line. You'll jsut run faster and longer during your "run" portion as you improve, but the run is always followed by walk breaks.
C25K is distance specific (it's specifically for 5K) where as JG is about running method (that can be for 5K, 10K, half marathon, marathon). It's a bit apple to orange, which is why it may sound confusing when you compare. I think JG is a great method especially if you weren't always athletic (I was a kid who always got picked last in gym class) - it gives me mental mini goals to look forward to. On the other hand, to some people to have a 1 minute walk break between running is a mental stumbling block...once they walk it's really hard for them to start running again. So it depends on the person really. I'd say pick one and give it a good try, see if it works for you. If not, try the other way - they are both good.
Sorry for rambling too long - hope this helped a little. Good luck!