2-3 minutes sounds sublime. What sort of lifts are you doing? I only have free weights at home and have struggled to find a good routine that doesn't take too much time.
The "big 3" are the core strength workouts of bench press, squat and deadlift. These are the workouts recommended by Rippetoe in Starting Strength: https://startingstrength.com/get-started/programs
For me this usually translates to one day per week of "upper body" (bench, abs, whatever ancillary stuff like curls or skull crushers) and one day per week of "lower body" (squat, deadlift, ancillary stuff such as calves). Abs are worked in between on both days, usually with body weight exercises. This is enough to keep me in good shape. If I do the above 4 days per week instead of 2, it's enough to get me into great shape.
All of the above can be done with a set of dumbbells going up to 20kg/50lb. You might substitute squats with lunges if you don't have access to a barbell.
Try to work towards the 1 hand 1 leg pushup, or planche pushups. Way better and more efficient.
My cardio (cycling) includes a mix of sprints of various sorts so I don’t bother weight lifting for lower body. Getting too bulky is also not good for speed in cycling so I’m not trying to get super buff so everything is just dumbbells and weight vest.