I think a lot of people have a difficult time knowing where to start when they decide they want to get healthy (for whatever reason). Should they go on a diet? Take some kind of pill or supplement? Have some kind of surgery? Simply eat better? Exercise (gasp)?
From what I've seen throughout my life, and based on my background in physiology, I'd say the only questions above for which the answer is a resounding yes are the last two. Optimal health requires sound nutrition and an active lifestyle. In the long term, there is no good shortcut to a healthier you. Sure, there are fad diets, medications, and surgeries that can help you shed some weight, but these either carry potentially serious health risks, or simply do not work indefinitely.
So, now that you know where I'm going with this--i.e., "Getting healthy is difficult"--you may still wonder whether you should start by jumping (or easing perhaps) into a vigorous exercise routine, or whether you should start by improving your nutrition. Getting healthy is "simple" but it's not "easy, " and there are as many best approaches as there are individuals, I think. There are a range of approaches that extends to pure exercise on the one hand, to pure good nutrition on the other, with myriad combinations of the two in between, and some range of combinations that will optimize health and fitness.
Exercise----Exercise/Good Nutrition----Good Nutrition
The question: Which side of the continuum should I start on?
The answer (in short): Whatever works!
Personally, I started with good nutrition, lost some weight and improved my health, and when I got more comfortable being active, I started exercising. Now I continue both because I like the way I feel and the sense of accomplishment. I also enjoy the support of many people I care about (and who care about me, obviously), and a vast online community of fitness-minded folks.
I know many people who have taken the opposite approach. Two friends of mine from high school started by simply exercising. The gains made through exercise piqued their interest in further possible gains, which led them to start making some changes in their diets as well. Nothing drastic, but things that should be helpful if they keep them up.
Of the two, exercise and nutrition, I think exercise is the easiest for people to get their minds around. People intuitively understand how exercise will help them, and they can see a direct cause and effect relationship between their exercise regimen and their physical fitness (strength and endurance). Nutrition benefits are often less obvious, or altogether intangible. You don't, per se, feel any different when a change in your diet drops your LDL levels, or increases your HDL/LDL ratios. If most of the benefits of exercise are obvious, most of the benefits of improving your nutrition sneak up on your so slowly they are virtually imperceptible!
One benefit of both good nutrition and exercise is very noticeable, however. Weight loss from either is obvious. To some extent, both occur as a simple change in the balance of calories used to calories consumed, too, but for weight loss due to nutrition, there can also be some effect of which foods we choose to eat. For example, eating a nutritional balance of fats, carbohydrates, proteins, vitamins, and nutrients should theoretically help you optimize your health in the long run much better than other eating options. Other eating options may result in more or less rapid weight loss, but they are unlikely to provide all the nutrients needed to optimize health.
As you can imagine, the best approach is to combine good nutrition and exercise, but to do both properly for maximum benefit, you have to climb a steep learning curve, and all along the route are snake oil salesmen, and marketeers trying to sell you a bill of goods, seeking to make money off your desire to better yourself, and hoping that desire will obscure your objectivity and critical thinking skills. We just have to do the best we can to navigate this mine field of useless, sometimes even harmful, advice and products. That's the nature of free market fitness.
So, back to the central question of this piece... Where should you start? I think you should start where you are most comfortable, because where you start has to meet three criteria. It has to A) work, B) be sustainable. In addition, you have to be ready to adapt as climb higher on that learning curve and gain new knowledge about health and fitness practices and new insights into your personal health and fitness quirks and needs. The tricky thing I haven't even touched on is how you have to balance your health and fitness practice with other responsibilities, mostly because I suck at it!
It boils down to what you're interested in. Are you interested in physical performance, improving your strength, and physical achievements. If so, I think you should probably consider starting with exercise. I suspect that if you can stick with it, you'll ultimately begin to learn about sound nutrition in order to improve your performance. If you just want to be a little more active, but primarily just want to improve your health, you might want to start toward the nutrition end of the spectrum. As you learn and your health improves, you may begin to find that some of those physical feats you never cared about before become more interesting. For example, I never considered running even a 5K race when I started getting healthy. I just wanted to be comfortable with a higher level of physical activity. After I lost some weight and started getting more active, though, my newfound confidence led me to commit to cycling 1000 miles during a single summer, and that led me to try running - at first to improve my cycling, but then for it's own sake. A year later, I'm still doing both and I've run several races and have plenty more on the schedule now.
No matter which end of the exercise-nutrition continuum you decide to start with, surround yourself with people you care about who also care about you and will be supportive and encouraging! It can't hurt.