You will need to build upper body strength and endurance for fighting. This will apply for boxing or grappling.
There is nothing better than simple bodyweight exercises like pull-ups and push-ups.
Here is a perfect training routine for building fighter's upper body.
4 Exercises:
All bodyweight but you could add weighted vest.
These 4 exercises are done as a circuit, one exercise after another without breaks until all 4 are complete. Rest for a short period of time and repeat for 3-5 sets.
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Fight Training From Home Programs/Courses
Whether you are a professional or a beginner, you'll be spending majority of your life training solo (from home or on the road). Working on technique, drilling, developing strength and cardio. I've been training all my life. Here are some of the best programs and courses to start or continue fight training from home.