What's your warm up??

[Howdidthathappen1]

I'm in process of sorting myself out after about 18 months out of the gym. Used to be an avid gym goer - I do (did) love a kettlebell.
I am seriously unfit now plus lost confidence. I'm OK starting low focusing on form but ridiculously I'm more concerned about an appropriate warm up as I'm very aware of potential for injury coming back from zero fitness
I used to spent 10 mins on the cross trainer then do a round with a very light kettle before doing the workout with 8kg and 10kg kettles (not that heavy I know!).
Does this sound OK? Unfortunately I do a bit of a ridiculous job with unpredictable hours so can't do a PT

You want to get good range of movement into the body parts you are exercising. For a general all over I would do:
2 or 3 sets of 5 reps of
bodyweight squats
bodyweight lunges each side
swinging leg forward and back (e.g. stand with kitchen counter on your left side, use left hand on counter for support, swing right leg up and forward as high as it will go 5 times, then back as high as it will go, then change sides)
swing arms to hug yourself (stand, elbows out to each side as if you were going to flap them like chicken wings, swing into a hug and try to touch your shoulder blades with your finger tips)
swing arms straight in front of you as high as they will go and back down
roll your shoulders and try to shrug them down as far as they will go (imagine you are trying to get your shoulder blades into jeans back pockets)

Then do the light round with the kettlebell and you should be good to go.