I train in a three day split with my brother. He's more into competative powerlifting but we work on similar routines since he's an instructor now as well. As far as exercises go if you're not going to be frequent, stick with the big movers: Squat, Deadlift (or sumo deadlift if you prefer), Overhead press are all good. I'd throw in a push and a pull for your chest as well so bench and row. Maybe some accessory work depending on how you feel? Your benefits are going to be down to your diet, base metabolic rate and how much rest you get between them, but if you're eating clean and resting well, you should benefit in some form. Some people only need to lift once a week, some need to lift most days to see any benefits. Humans are funny like that
If you want to get strong and the gym has powerlifters or guys who can pull over 250kg and squat 200+ go speak to them, the best way to get strong is to hang round and train with stronger guys, its not difficult but the problem is everyone in the internet age has an opinion but not all opinions are valid. Likewise if its s and c for MMA you are after speak your coach he will know more about it than most here
I've done quite a bit of caveman exercises before. I know there is a really good book on it somewhere on it. They even have a Grappler and stair climber there. Not too many Douche Bros there either.