I feel for you. I had a similar starting place at the beginning of this year. Bad back pain, 60 pounds overweight, little knowledge of fitness, etc. Back pain is actually a great motivator to exercise: with the right set of exercises, I can get fast improvements in pain so that I actually have something to remind me to exercise. Back pain is sort of like a really obnoxious gym coach. :-) Here's what I've learned so far.
Back Pain: I'd recommend Yoga. It's been tremendously helpful for my upper and lower back pain. (Since you're a university student, I'd note that my alma mater had free yoga classes available for students, not that I ever went to them.) In addition to the back pain exercises mentioned by @Informaficker, I find crunches helpful for my lower back. See also the pelvic tilt/curl Pilates exercise, which is simple but very effective for mobilizing your lower back and strengthening weak muscles there. If your gym has one of these, use it. It's very helpful in strengthening your lower back muscles, and you can also use it to strengthen your lats. It's not particularly difficult, and easy to scale up/down on as pain requires.
Aerobic Exercise Reasonably intense exercise doesn't have to be high impact. If you struggle with maintaining exertion over 4-5 minutes, try going slower with less impact. While HIIT (high intensity interval training) gets a lot of press, the fact is that it's really hard. You can get a lot of the benefits of cardio with less intense exercise, and work your way up. The important thing is to find anything you can actually do that leaves you somewhat out of breath while you're doing it. Keep doing it for 20-60 minutes. For me, that's a brisk walk on a treadmill at a very steep incline. I started walking at a 5% incline and 3.2mph for 30 minutes, and have worked my way up to an 11% incline at 3.9mph for 50 minutes. It's not super-intense exercise, but I'm usually drenched in sweat by the end. I usually even read a book while on the treadmill.
Diet and Weight Loss Despite losing around 40 pounds so far this year, I actually have little idea what the "right" diet is for weight loss. I'm not sure there is one, or at least one strongly supported by the evidence as both healthy and effective. (Low carb diets are apparently effective and possibly healthy, but I found low-carb almost impossible to stick with while having a life.) As you'll see below, my diet is so-so: for me, exercise seems to be the key to weight loss.
The only bits of advice that I've found that seem effective Protein leads to satiety. I try to eat unsweetened greek yogurt (look for something with ~75% of calories from protein), tuna fish, boiled eggs, lentils, etc. I would advise finding some high protein foods you enjoy and eat mainly those. Bread is not particularly high protein, but most lean meats get a very high percentage of the calories from protein. Monotony reduces hunger. I try to eat the same small set of things. Things I enjoy eating, but the same things. That probably sounds depressing, but if you pick the right set of foods it's not bad.
@Informaficker is definitely right that weight tracking is a good motivator, and that sugary drinks are bad (switch to tea, coffee or water). For tracking, I like The Hacker's Diet website. It's bare-bones, but it automatically produces an exponentially-smoothed moving average of your weight, which smooths out day-to-day variations (mostly water and bowel movements), and shows you the real trend over time. Seeing that trend line react to things you eat and exercise can really be very motivating. It's important that you weigh yourself at consistent times, and preferably close to naked, or the signal will be much noisier. Different clothes can vary significantly in their weight, and I've seen my weight fluctuate by 2-5 pounds over the course of the day. It's much more consistent first thing in the morning.
Note that it will probably seem like you aren't making much progress, even when you are. Weight loss of 1Lb/week equates to a 500 calorie/day deficit, which is a lot of work and great progress. But 1Lb/week is nothing compared to day-to-day fluctations of 1-5 pounds. You can only see the trend over time, so don't get discouraged by setbacks and fluctuations. Even half a pound per week is still 26 pounds per year!
Finally, here's what I usually do in a week:
- Bike to work every weekday, 4 miles/day.
- Monday, Wednesday, Saturday, Sunday: 1 hour yoga class, 40 minutes of crunches, pushups, weight-assisted pullups, arm circles with hand weights (5-10Lb) and the reverse-situp machine mentioned above. 50 minutes on the treadmill at a brisk walk with a steep incline.
- Breakfast: 1/4 cup (dry) oat bran hot cereal, with berries, walnuts and milk. Some vegetables on the side: eg carrots, kalamata olives. Coffee with heavy cream, no sugar. Four fish oil capsules. Sometimes I eat Greek yogurt instead of the oat bran.
- Lunch: Usually crappy restaurant food. I try to forego starchy sides, notably ask for Asian food with no rice.
- Dinner: Frequently lentil soup, rye crackers, and goat cheese or yogurt. Lentil soup is one of the few things I cook because it's very filling, is insanely cheap, and is easy to make lots of leftovers. Four fish oil capsules. Usually a few glasses of red wine.
- Snacks: I avoid snacks as much as possible. I go for either fruit (apple, orange, berries, banana) or yogurt when I lose resolve.