I would say don't feel like you have to start doing everything at once. If the gym is too far away, try doing a workout DVD or program you can do at home. There's a lot you can do with some simple, inexpensive equipment like a mat, hand weights, pilates ball, stretch bands, etc. Pilates is great for strengthening your core muscles. That stuff isn't really required to work out at home, but I like the versatility, almost as good as having a real home gym. A lot of moms enjoy doing "mommy-and-me" workouts that incorporate their babies using them as weights, like this
. Pushing a stroller is a good workout. Don't discount the good, calorie-burning exercise you can do without going to the gym.
As for the hypothyroid, there's not much to do but get your labs checked as recommended by your doc and working him/her to manage the lab values and symptoms. I gained a lot of weight before I was diagnosed, but I had been that heavy before and attributed the gain to the stress, poor eating, and sedentary lifestyle I slid back into once I became a student again. I'm feeling well enough to have another go at weight loss now, but it definitely seems harder and slower than when I started losing weight the first time around 7 years ago.
I know how hard it is to put down snack food that I should not be eating, so I generally don't have it in the house when I'm trying to lose weight. I also like to cook big batches of food when I have time so I can eat the leftovers when there's no time to cook.
Good luck! What graduate degree are you working toward?