Exercise is a wonderful thing regardless of your weight. It has HUGE benefits for your cardiovascular system, which is important because T1 diabetics are at an increased risk for cardio problems. It is also proven to help with mood and overall feeling of well being (you release endorphins when you exercise, which is your body's natural way of making you feel good!) And, exercise will have huge benefits on your blood sugar levels.
I think you have to find what exercise plan works for you and your lifestyle. Some people really like to have designated times of the day for exercise. You can start by just going for a walk/light jog. Make sure you have good/proper shoes for walking/jogging. It's a cheap, easy way to get in some exercise. Stay in well-populated areas, wear some identification that says you're a T1 diabetic, and always carry fast-acting glucose with you (and a meter if you can).
Experiment with the right temp basal setting. Check your BG before, during, and after exercising. I have found through lots of trial and error that a temp basal setting of 0.375 generally works best for me during exercise. I have to remember to turn it down about 30-60 minutes before running, otherwise I need some carbs to get through my run.
Strength training is also good; increased muscle mass can help bring blood sugar down as well. The good thing is that you don't need a gym to do this!! There are plenty of basic exercises you can do right in your home (sit-ups, push-ups, etc). Look online for isometric exercises, which use your own body's weight.
Yoga is also good. Yoga DVDs are available through Amazon.com. All pretty affordable.
One thing that helps me is that I see my exercise time as my personal time. I love going for runs/walks because it's my time to be alone and just think. I listen to music (I love making playlists for running) and have a sort of personal meditation.
If you're on a pump, that makes exercise much easier. Be patient and start slow, but if you stick with it, the results are awesome.