In my opinion, one should never work themselves up to a machine. In fact given the choice between a free weight movemnent or an equal machine movement, always opt for the free weights. The only machines I use are for lats as in pulldowns and cable rows and those are usually only after barbell rows and dead lifts. If you are just starting out, stick with the core/compound free weight lifts. You will make better progress if you do..
1) Begin with the most technical of your lifts, as these are generally the most taxing, both in terms of forces and load, as well as a greater energy requirement simply to maintain proper form. Power Cleans before Deads before Hyperextensions, for example.
2) Begin with the lifts/bodyparts you want to give the most growth/strength (attention) to, if any. If your quadriceps development is lacking, do your Squats first, for example.
3) Go from least stable to most stable. Dumbbells are obviously much less stable than machines, so they require more energy for the coordination of their movement. If you are to do, for example, a Dumbbell Shoulder Press and a Machine Shoulder Press in your routine, do the Dumbbell Shoulder Press first.