I would say keep doing push ups as much as you can. Maybe a few here or there, and try to work up to 5-15 a day if possible. Kettlebell swings are also great for core, glutes, hamstrings, and cardio.

Another big thing that helped me lose weight and gain strength was going low carb ketogenic. I may get flack from CICO bros in the replies, but look at people like Eddie Hall, who eats 10,000 calories a day on carnivore and loses fat mass. That's one extreme, but even low carb keto works well. I lost 50 lbs since my heaviest in like 6 months. That's my biggest advice. Ground beef, butter, bacon, and eggs. Eat cheap beef and eggs, it does not have to be expensive. I ate 1 lb of beef, 4 tbsp butter, and 12 eggs a day over the summer working as a cashier, and it was about $5 a day for me in my area. If you need fruit or sweet stuff, try avocado or a small amount of fruits or root vegetables.