I might be giving advice opposite a lot of people here, but I think you need to pump the brakes.
I wouldn't make any major changes in your life, tracking macros, doing x sets of x reps @75% of 1rm, downing 3 scoops of metabolic whey 60 at every meal, going vegan/paleo/gluten free, mixing c4 with your BCAAs, daily or before/after workout weigh-ins, that's all great for a certain crowd... but I don't think it's right for you.
I would compare you starting your journey (not sprint, not dash, not your forgotten-by-march-resolution) toward physical well being to my journey in mustachianism. If you don't already go for a walk in the morning, and weather permits, go for a walk. Have your coffee first if you want, maybe a bite of breakfast to take the edge off, but before you start your day, go for a walk. Don't aim for a pace, don't count your steps, don't track it with an app, just walk around your neighborhood. Walk a quarter mile, a whole mile, probably not much more than that at first. Take the time to think about why you are walking around your neighborhood, about all the forces in your life that have brought you to this one moment. I like to use my morning walk as a way to meditate on my actions, examine the path my life is taking, and decide what I can do that day, to make sure my life goes the way I want it to. Don't make any crazy changes until you have done this for a month or so, you will know when it finally becomes a habit better than any of us.
At the same time, or shortly after, start working on your push-ups. Do 5 whenever you think about it, again with the walking, don't keep track, don't monitor every action with an app, just do push-ups when you think about it and have the time. Maybe do a plank before your push-ups, or after, or both. It doesn't matter, just do things with your body, toss in some air squats after you're done, keep your back straight, eyes on the horizon do 5 or 10, whatever is comfortable... comfortable, we will revisit that word. The point isn't necessarily to follow someones 30 or 60 day plan, to follow what the magazine says to get 6 pack abs by summer, it sounds like you just want to be a fitter human being, and that is a marathon, no need to rush.
Before you start doing exercises, do some research on proper form, even as a beginner just using body weight exercises, using proper form is imperative. If you can't continue the exercise with proper form, stop. Do some later instead.
As for the diet aspect, hydration is extremely important, and often overlooked. Every aspect of your body needs water, and when you start exercising more, you are going to make your muscles thirsty. Drink lots of water, but don't drink too much. I don't measure my water intake (usually) but if you don't know where to start, I'm sure some scientists have made a calculator based on your age/gender/weight/etc. There are a lot of diets out there, I personally dont subscribe to any. I do juice (vegetables, think Fat, Sick, and Nearly Dead) daily at lunch, but I also eat food at lunch. It is a supplement for me, that's another word we will have to revisit. That is about as extreme as my diet gets, aside from my abstinence of fast food whenever I can help it, which might not be extreme here on these forums, but seems to be in daily American life. I just try to eat healthy things, baked chicken instead of fried chicken, a good balance of proteins and carbs and fruits and vegetables. Someone mentioned smoothies earlier, and how they were bad because they have so much sugar. I would like to respectfully disagree, sometimes I like to take smoothies as a "pre-workout" because they have lots of carbs and sugar, which is a pretty efficient way to give your body energy. But yeah, too much of anything in your diet isn't a good thing, so don't go crazy. Don't give up beer or wine or coffee. Maybe give up or cut down on soda and energy drinks if you currently consume those. I like to have a coke every once in a while, but I'm talking once every couple weeks.
Comfort and supplements. First, you are forging your new body like a blacksmith forges a sword. You aren't painting happy trees with Bob Ross. Eventually, you need to make yourself uncomfortable to see progress. Don't exercise if you are hurt, recovery time wont help you progress, but make yourself uncomfortable when you are exercising. Supplements, please stop taking whatever protein you are taking. There is no need for you to supplement at this point. Supplements are meant to "supplement" your diet, to provide nutrients you can't get through eating normal food in your normal day. Please do me a personal favor and stop taking them at least for now. The one supplement I would ever recommend to a beginner is a BCAA with no caffeine. I prefer AMINOx by BSN, I don't work for them or any supplement store or company, but I like the product. I would ask that you do your own research, and decide what is right for you. Also with everything else, don't let your sole source of information be someone working on commission.
I didn't mean for this to be such a wall of text, but I hope it helps.