You shouldn't train only your chest and not your back or you're going to get all imbalanced.
Also you don't have to use only pushups because you don't go to the gym. You can work your whole body in a manner that continues to be challenging, at home and without a lot of expensive equipment. Once you can do 10-15 pushups (which is fairly quick to be able to do) pushups will become too easy to be challenging if you stay in the recommended rep ranges. You need to use a progression scheme for each exercise
It's also a good idea to use a program that has already worked for many people instead of throwing something together on your own
This comment is heavily ripped off from https://www.reddit.com/r/bodyweightfitness/wiki/kb/recommended_routine
The only equipment you're gonna need is a pullup bar and eventually gymnastic rings. Gymastic rings are light, cheap (~20-25$), easy to carry around, and very versatile. You can hang them from your pullup bar, from a tree or anywhere really
If there isn't anywhere for you to hang the rings and you don't have a pullup bar, drop the dips and pullups, and replace the rows by resistance band rows (these are also pretty cheap and they don't require something to hang)
For the pairs, you're supposed to do one set of the first exercise, rest 90s, do a set of the second exercise, rest 90s and start over.
For the progressions, you're supposed to choose the exercise that you CANNOT do 3 sets of 8 reps of. When you are able to do it, you go to the next exercise on the progression
* = see below for the condensed version, see the link to the recommended routine for more info and videos
Monday Wednesday Friday:
Warm-up dynamic stretches*
Warm-up bodyline drills*
Warm-up: 20 burpees (if you're not already warm)
Support practice*
Handstand practice*
First pair: 3x5-8 Pullup progression* + 3x5-8 Dip progression*. Skip this pair if you can't do 3x8 diamond pushups and 3x8 horizontal rows yet
Second pair: 3x10sec-30sec L-Sit progression* + 3x5-8 Squat progression*
Third pair: 3x5-8 Pushup progression* + 3x5-8 Row Progression*
The warm-up dynamic stretches routine (~5min):
shoulder rolls
scapular shrugs
cat-camels
band: straight arm overhead pull downs
band: straight arm chest flies
band: dislocates
wrist mobility exercises
front and side leg swings
Bodyline drills
60s Plank
60s Side Plank
60s Reverse Plank
60s Hollow Hold
60s Arch Hold
No resting in between the holds
Support practice
Parallel Bar Support (can also be done on the back of 2 chairs)
Ring Support Hold
Rings Turned Out Support Hold
Handstand practice
Wall Plank
Wall Handstand
Freestanding Handstand
Pullup progression
Pullup negatives
Pullups
L-Sit pullups
Bar pullovers
Dip progression
Parralel bar dips (or negative ring dips if no parallel bar available, or dips between 2 chairs, or dips in the corner or your kithen counter)
Ring Dips
Rings L-sit Dips
L-sit progression
Foot Supported L-sit
One-Leg Foot Supported L-sit
Tuck L-sit
Advanced Tuck L-sit or One-Leg L-sit
L-sit
V-sit
Squat progression
Assisted Squat
Squat
Step-ups (one leg)
Deep Step-ups (one leg)
Pushup progression
Vertical Pushup
Incline Pushup (lowering the incline over time)
Full Pushup
Diamond Pushup
Rings Wide Pushup / If no rings -> pseudo planche pushups (PPPU)
Rings Pushup
RTO Pushup (Rings Turned Out)
RTO PPPU
Row progression
Vertical Rows
Incline Rows (lowering the incline over time)
Horizontal Rows
Wide Rows
Tuck Front Lever
Tuck Ice Cream Maker
Tuck Front Lever Row
Advanced Tuck Front Lever Row