@newbeginning1996 What you're doing is perfectly fine, and is pretty close to what I do for barbell lifts, chinups and dips.
For barbell work, chinups and dips I like to do a pyramid. So I might squat or press the bar for 20 reps, 15 with a bit of weight, 10, 5, 3, 1, and then do my working sets. If I've already done a sufficiently similar exercise I don't bother - for example, I don't warm up for shrugs after deadlifts.
For chinups and dips I'll do a somewhat hard set at bodyweight (sometimes I'll go to or near failure to gauge where I'm at), then proceed to pyramid with weighted sets.
I never warm up for kettlebell work. In the kettlebell world I'm moving some pretty decent weight - 2x40kg for clean & press and front squat, 1x40kg for snatch - but I always feel ready to go straight to the working weight, unlike with barbells, chinups and dips.
I don't warm up for burpees or pushups, including one arm pushups. I don't do a general warmup - the warmup sets are there to get me prepared for a specific lift, and stretching and treadmills don't do that.