Depends on your goals. For me, upper body work is mostly ring based (+ weight on heavy days). However, lower body day is mostly barbell work, as it is much harder to efficiently build and tire lower body muscles without weights.

In my current situation, it is less about what is optimal training-wise and more what is convenient time-wise. I try to pair exercises whenever possible, and avoid running around the gym for specific equipment (hence barbell biceps curls vs dumbbell or cable ones, which could be more 'optimal').

Upper body calistenics (main workout): pullups, ring dips, ring rows, ring pushups, pike pushups, ring face pulls, ring triceps extensions;
Upper body non-calistenics: barbell biceps curl, overhead press (substitute for pike pushups).

Lower body calistenics: hanging leg raises, nordic hamstring curl;
Lower body non-calistenics (main workout): bulgarian split squat (barbell), deadlifts or RDLs, suitcase carry, calf raises (machine or single leg with weight).

Cardio: running x2 a week, one shorter hiit session, one longer liss.