I think the first questions have to do with your current fitness level, your goals beyond PRS, and the amount of time you can invest in exercise.
Starting off at a low level, establishing a simple step goal and hitting it each day with the most basic movement (walking) is going to pay off in many more ways that just rifle shooting.
Beyond that, what I would call "intentful cardio" is beneficial. Pick an activity - running, swimming, cycling, rowing, whatever - and try to get your heart rate up for 20-30 minutes a day. You'll get used to performing a basic function with elevated heart rate, and eventually there are some adaptations that occur which will decrease your heart rate for a given amount of exertion. Once again, this has benefits that go way beyond running around with a rifle.
Some combination of resistance training - bodyweight, iron, machines, whatever - and cardio would be the next evolution. Over the past year, I've incorporated exercises from these guys into my routines:
449K Followers, 782 Following, 2,170 Posts - See Instagram photos and videos from Joel Seedman (@dr.joelseedman_ahp)
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The World's biggest biking photo gallery of photos like, crashes, north shore. OHDS test- full pass
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92K Followers, 947 Following, 330 Posts - See Instagram photos and videos from CombatStrengthTraining (@combatstrengthtraining)
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There are thousands of other trainers on social media, and some of my buddies have busted out their old P90X DVDs in the last few weeks. Once things get back to normal, I'd suggest finding a local trainer who has experience with clients of your age and condition. There are endless ways to combine weights and cardio, and with a bit of creativity, it's possible to get large benefits with minimal investment of time.
Really, there isn't going to be much about training for PRS that doesn't also carry over into a bunch of other activities, so you're not looking for anything specific - you want some aerobic conditioning so you're not sucking air after every transition, you want some strength so that you can hold a heavy-ass rifle while maintaining a variety of positions, and you want some flexibility. That's fundamentally not any different than the average middle-age golfer or the guy who wants to play hoops with the younger guys at his gym.
Good luck!