Minimalism is cool when you have a lot on you're plate. You guys know I hate terms like "optimization" and "most efficient" but sometimes you really do need to pare things down to a minimum. That's what I've done here for guys who spend time on the mats. I feel like this could be beneficial for strikers as well seeing that their posture is similar and they they spend a lot of time with anterior motion. Anyways here are my 2 moves I tell folks to do if they are rasslin and either hate lifting or "don't have the time" (most times this is a cop out). I chose them because they are easily accessible, readily available, and provide some much needed balance.
Karl Gotch was the man for S&C back in the day. Hell I bet you've done his playing card workout.
Chinup: grappling is ton of upper body pulling, so naturally you need to be strong in that motion. Chinups or Pullups offer some other benefits as well such as Grip work (strong hands are beneficial for anything in everyday life) and spinal/gluteal humeral traction (hanging basically decompresses your spine and opens up your shoulder joint, which every grappler I know has at least one bum shoulder). Chins can also give you some big ass arms, source: gymnasta. Rope climbs are a great alternative for some added variety, and if you plan to do these daily I'd do them on rings to allow some freedom with the shoulders. I've noticed that for me using a straight bar all the time tends to aggravate my elbows. So listed from best to worst in terms of elbow health for everyday pulling: rings, neutral grip, underhand grip, overhand grip.
Both stances are fucked for your back
Kettlebell Swing: man I love these. Swings strengthen your whole back side, and I'm all about that rear view. Glutes, hams, lats, traps, erectors... if it's back there it's getting hit. Now for BJJ guys and wrestlers who spend a lot of time hunched forward, this will help balance all that out. Again swings also offer a grip training effect, but also a strength endurance component. Strength and endurance is the ability to produce high relative force over a longer duration then what would be considered anaerobic. That's my definition anyways. It's akin to the cardio you need on the mats, but nothing is as good for grappling cardio than grappling more. Kettlebell snatches or cleans are good variations as well, but they are a bit more advanced. If you find you enjoy kettlebell work then by all means dive off into any ballistic move you'd like for this movement. Of you're really afraid of swinging then the single arm kettlebell deadlift is a good alternative till you learn to swing effectively. Setup: as for sets and reps you can go a few ways. I personally like the "aftermath" setup where I do 3 sets of max reps on chinups, then 5 sets of 10-20 reps on swings. Another alternative is to select a number of reps or sets for each and do them throughout the week. You could say "I need to do 15 sets of pullups and 500 swings this week" and break them up accordingly. This method requires some math and log booking so if you aren't into that I would avoid this method. I will say this method allows for more trackable progression though, since you can increase reps/sets progressively. To sum it all up, you can never go wrong with pulling for fighters of any kind. They all spend a ton of time hunched over and pushing/posting/punching so it's good to negate all that anterior stuff with some posterior stuff. Good luck on the mats.