C25K, where to start?

What is your end goal? that is honestly the most important consideration. For me, the end goal is just to be a runner. I want to run a 5k, get used to that, and keep on working until I can run a half-marathon. For this reason, I run outside. Even if I do go to a track a lot of the time, it's important to get used to being outside. The weather makes a big difference, and dealing with external stimuli like other people and needing to control your path are important. Plus, when you're on the treadmill, it's actually easier because the belt is moving and propelling you forward, whereas outside you have to work on propelling yourself forward and setting a pace. Your treadmill work should help you with that.

If you're perfectly fine with running on a treadmill your whole life and not doing races, stick to your treadmill and just keep increasing your pace as you feel like you can. I'd recommend getting a heart rate monitor so that you know what speeds work you out the most. You can easily look up the info for heart rate stuff, and it should come with whatever monitor you end up getting. I got the cheapest one available on Amazon, which was an Omron unit for about $30, and it works wonderfully.

If you want to run that 5k, hit the road and get used to training for it. A lot of people report that it's harder to run outside than it is to run on a treadmill. You wouldn't necessarily need to start over with C25K, but maybe put yourself in there at week 4 or week 5 and see how you do outdoors.

Should I even bother doing the program or just keep increasing my speed/distance?

I'll go out on somewhat of a limb and say you don't need to do the program. But, I would definitely advise running outside on the road or a track. It's a different ballgame. For some reason, when I'm on the treadmill, my comfort zone is a 12-minute mile. When I'm doing a run of about three miles, I'm at a 9-minute mile.

If you find it easier to run on the road (and not everyone does), that mile on the treadmill could be 1.5 miles outdoor. Then, it would not take much more to get to two miles. If you can do two miles pretty consistently, you'll be able to do a 5K. There's a boost that you get from being in a real race situation and that will give you the extra even if you're not yet at the level to do 3.1 miles on a regular basis. Sounds like you're doing just fine now!

Good! If you have a heart rate monitor, you already have the key to starting your outdoor workouts. I hate the heat and I hate sweating, and despite living in rural South Georgia where there are literally 0 times you're ever going to go outside and find humidity under 80% (it usually sticks at 100 >_<), I have gotten used to running outside.

For you, I'd say start on a track, and throw your time numbers in the garbage. They aren't applicable. Use your HR monitor, and try to stick at a pace that gets you around 60-80% of your max heart rate, which at your age would be 113-150 bpm. Ideally, you'd keep it in the middle at about 135ish as you work on upping your mileage. Higher heart rate is not better, so don't push it! You can literally be nearly shuffling at the speed of snail, thinking, "Well I can walk faster than this!", but as long as you're running and it's in that comfortably HR zone, you're progressing.

From what I've read, it's recommended that until you can comfortably run 4-5 days a week and 15 miles a week, consistently, adding distance and ignoring speed work is going to be the best thing for you to do. Some people recommend adding distance for even longer, or adding time (like getting up to running an hour each one of those days and 2 hours on just one of them for your long run, and doing that comfortably for months before you ever mess with speed work). I'm still in that phase now where I'm adding time and distance.

As for dealing with weather, I do what I can to run at dusk. I google sundown times for my city and arrive 45 minutes prior to that time so that I can get in my warmup and most of my run as the sun is setting. If it's raining, I usually still go as long as it isn't dangerously storming. A little rain can be very refreshing in the summer heat. If you don't like the track, hit a neighborhood and be sure that you aren't going out of your HR zone on inclines or hills. You have to slow it down or even walk those hills, but that endurance is so important!

I love how far I've come on my way to becoming a runner =D. In 2 months I've lost only about 3 lbs, and I still have plenty left to lose, but the benefits are very rewarding even if my body is too stressed to be losing weight right now. I, too, would love to be able to say I ran a marathon someday . Good luck to you, and if you ever have any questions, feel free to ask! I can't promise I'll know the answer, but I do know a lot of runners, so maybe I can help you find it.