A couple thoughts:
The ultimate difference between a guy and a girl routine is the weight itself.
Warming up is important and there are several ways to do it from super light weights, cardio or stretching, depending on her goals.
As a beginner she may enjoy a few key moves- compounds. They tend to have a pretty good full-body recomping effect, however what is most important is what she finds enjoyable or fun. When I first began at the gym- I had a routine that included:
Curl Machine, Ab workout (crunch and reverse crunch), Smith machine overhead presses, Pec deck (i think its called), Bench press, Tricep rope thing, Lat pulldown, and Rows (i didnt do legs because I long distance cycle).
The circuit style routine was: set: 3x and reps: 10,6,8. lighter/heavy/medium.
However she could benefit from the traditional 10,8,6 as well. Or any combo-
I chose the 10,6,8 because I felt I got best of both worlds- reps and weight. So - that I wasnt tired by my last set I moved the heaviest set in the middle- and closed with a medium weight for medium length.
for aided fatloss- you can superset a pair of workouts, because it requires a certain level of endurance...as I am sure you have felt that your heart rate increases after a superset.
This routine helped me get acclimaited to weights, as well as gave me an overall understanding of the kinematics of training.
I think its important to use free weights, however I think that using machines really helps understand the way your body works as they are designed to be user-completed-machines. That is they cannot work without a specific movement that is provided by the user. Machines IMO, teach good form. Machines can also be fun/entertaining for a beginner.
Another encouraging thing is having a training partner (you)- trust me it can get very boring some days when you always train alone or dont know anyone at your gym.
Best,
A.