What I mean by doing the basics right is that if you're out of shape, there's no need to be guinea pig.
Eat or drink less of stuff that has too much or too quick energy i.e. fat and sugar. Avoid too much alcohol. Eat normal amounts of protein and carbohydrate with high GI and drink water, keeping you from having cravings. Exercise both anaerobically and aerobically, with warm-up and stretching. Get enough rest. Do it all regularly and measure the progress.
First, the crowd there acts as an informal support group. Seeing others working hard to improve their own health is motivating for oneself.
Second, a gym offers much more than simple pushups can offer. Sure, pushups are great for getting started, but you'll eventually grow strong chest and triceps muscles and the rest of your body will fall behind.
The gym you attend is also important. I drive ~15 minutes to the nearest Gold's Gym, because the local Palo Alto gym (4 blocks away) is basically a rich housewife's social club. Gold's is packed with serious lifters, and only $10 (!). It makes a huge difference for me; definitely the difference between going and not going for many, I think.
... and embrace whatever helps you do this, instead of shoehorning yourself into the "best" approach. Know yourself and know what works for you. Don't sweat it if the thing you enjoy doing several times a week is different from the thing all the cool kids are doing.
You can't call that getting the basics right, as if it's some well established fact. Citation needed.
EDIT: The modern diet, with all its refined white flour, has a much higher GI than in the past. (White flour has a much higher GI than fruits and vegtables, for a start). What do you think is responsible for the rising diabetes epidemic?