I'm going to disagree that the bar for going to the gym is 40 pushups/squats in a row.
MOST people can't get to 30 pushups in a row. Including top tier actors and fitness people. (I seem to recall a Jason Statham push up challenge video where he did about 27 before he was done. And Jason Statham is pretty damn fit.)
After a year and a half my best is about 22 or 23 pushpus (with rest pauses) in a row before I'm completely tapped out. I'll do 30 to 40 pushups for one exercise, but that will be broken up over 3 sets. (I think I could manage 40 air or box squats in a row with no weight pretty easily though.)
That said, I mostly agree: start with body weight exercises. Especially if you've never lifted at all.
WITH the caveat that your body fat is low enough. As I've said elsewhere, if you're struggling to do push ups at 20% body fat, doing them at 30%+ body fat is pretty much out of the question. As are situps, squats and a lot of other body weight exercises. You simply have too much body weight and not enough strength at that point. If you're carrying too much body fat, you pretty much have to start with walking or some light treadmill work, to get your body fat lower, so body weight exercises are easier.
But there's a lot of benefits to body weight exercises; people need to get acclimated to working out, both from a physical perspective and an mental/emotional one and getting started in the privacy of your own home can help with both.
I'm starting to do some very informal coaching with a few people here at work, and the #1 barrier to entry I've seen so far is ego. No one wants to look weak, no one wants to have anyone else see them really struggle. Nobody wants to fart while working out when there's someone else around. Our egos prevent us from really committing, and starting your body weight exercises at home is a great way to start building up that confidence (and more importantly, DRIVE) to be successful with fitness. I worked out for a solid 6 months only at home and at my work gym where I was the only one there. As I lost body fat and started progressing, that gave me the confidence to go to a gym.
Now....I'm getting to the point people are noticing. I'm getting comments. People are starting to come up to me ask questions. I literally had a woman I've been working with stop and look agog (and eventually reach out and touch) my triceps because I've been working them hard the last couple months, and between that and my falling body fat they're really starting to pop. That's like.....huge for your confidence and ego, when you've reached the point where other people are starting to notice and react involuntarily too it. (I'm not humble bragging here but the ladies have started to get kind of handsy with me the last few months, heeheehee.)
So these days.....IDGAF who is watching or what they see. The only time I care is if I'm doing something wrong or using improper form, at which point I welcome someone trying to educate me. Otherwise....I'm the zone and the only real thing I struggle with is uh....keeping my eyes to myself
My desire to progress and have access to things that will help me progress outweighs any self-consciousness I might feel about my body or my strength. Now I just go to the gym and work out like a savage, and try to get as close maximum intensity and failure on every set that I do. I get some looks every once in a while, but I'm beyond caring what the reason for those looks are. Maybe they're impressed. Maybe they're intimidated. Maybe they're aghast. Maybe they think I'm just a tryhard. It honestly doesn't matter to me anymore.
Because at the end of the day, this shit ain't about them. It's about you. Everyone in the gym is just as insecure and self-conscious as you are, even if they're ripped or whatever. Everyone struggles with these feelings.
momentum
This is really what it's all about at the end of the day. A body at rest tends to stay at rest. A body in motion tends to stay in motion. It's like getting a car rolling on a flat surface by pushing it. The hardest part of it is getting it moving and building some momentum. Once it's rolling, it becomes drastically easier to steer it and keep it moving. Fitness is the exact same way, in what I've experienced. It takes less effort to maintain a workout regime than it does to start or restart one. There's also a mental component to momentum. You feel better when you stick to it, it becomes a daily routine like brushing your teeth or taking a shower: you eventually just allot time for it like you would anything else.
Last bit of advice, chest expanders are phenomenal pieces of kit. They're really cheap and you can do a ton of exercises with them at home/on the road.
I'd say resistance bands are a better choice. They may not have grips but they're better designed to accommodate anything, from actual exercises to assisted stretches and all sorts of shit. They're probably a bit cheaper too.
Also I just did a 185pnd deadlift. First time I've deadlifted in 20 years. I'm very pleased. I went in thinking I'd be happy if I could do 135, but the person I was lifting with encouraged me to go harder. Not sure I could much more than that (185 is my body weight) and in the world of deadlifts 185 doesn't even register. But it's a Personal Record for me and I'm quite pleased because now I know where my functional strength stands with dead lifts, and I have a basis to move forward from. And I'm very grateful for the person I was working with, who primarily does squatting and deadlifting. His form tips and techniques very quickly showed me a properly executed deadlift SHOULD feel, versus how much harder and unpleasant an improperly executed one is.