Machines or free weights: where should you begin?
Choose equipment you can set up and use for your purpose.
Begin with the task
Ask which movement you want to practise and what equipment you can use consistently. A barbell, dumbbell and machine may all offer resistance, but their setup and movement constraints differ. A useful choice depends on more than how impressive it looks.
Machines still need adjustment
A guided path does not automatically fit every person. Seat position, handles and starting position affect the experience. Record useful setup details separately so you can reproduce them. Do not assume that the number on two different weight stacks represents an equivalent task.
Free weights need their own setup
Think about how you will pick up, position and put down the equipment. The working repetitions are only part of the task. Choose a setup you understand, and obtain instruction when you need it.
Avoid a universal ranking
The ACSM update does not identify one equipment category as consistently decisive for outcomes in the average healthy adult. That broad finding does not mean every exercise is interchangeable. Specific skills and personal circumstances still matter.
Compare like with like
In your log, keep machine and free-weight versions as distinct exercises. A larger stack number is not proof of stronger performance than a smaller dumbbell number. Consistent naming and recording make your own progress easier to interpret.