I mean you can really get by with just nothing, but it is helpful to have a home gym.
You can do these with no or minimal equipment:
push - push ups
pull - pull up
overhead press - handstand
leg movements - squats
Minimum equipment nice:
pull up bar
bar - power cleans, dead lifts, snatch
squat rack - squats, bench press
odd shaped objects
why buy equipment?
makes it easier
makes it different
makes it more difficult
do you get points for having the most spartan workout equipment
or do you get points for having physical results
or do you get points for being strong without much equipment
Workout everyday. Life will necessitate rest days. But workout everday. 4 different workouts. Keep experimenting, keep learning, keep exploring. Something better than nothing. Today is the only option. Consistency and discipline. Have fun. Work hard.
push - push up and dip
pull - pull up
squat / leg day
secondary - support
gut - aka core work
There are many different ways to do the given primary work.
But these are the basic building blocks for a person that can run, jump, fight, ideally you also learn to swim.
After these workouts, go do something fun. Something engaging that you like. Might be ride a bike, go on a walk.
The metabolic conditioning at the end is nice because, well, it is a workout. I think that having gut aka core workout at the end, is an even better order, personally. Because that is where you get the goods.
How many reps?
Do something. Just honestly do something. 4x6 or 5x5, or 4x12, 1 RM. Mix it up. Learn experiment. Your body needs and wants all of it.
warm up more - full body, wall sits, ball throws, accessory
primary work - interval workout rounds with finishers, 5-8