For an eliptical cross trainer. I would start out at 20-25 minutes and add 3 min a week until you reach 40 minutes.
Then you can lower the duration back down to 30 by alternating resistance so that you have one minute high resistance. three minutes low. Eventually working into 40 second sprints at high intensity and 2-3 minute breaks inbetween (This would be after three months).
What are your restrictions?
EDIT based off comment:
So the cross country ski machine will be great. You might consider getting a basic heart rate monitor after awhile... Nothing fancy... make sure it has a chest strap though... Polar and Suunto and others make nice ones...
It will tell you your heart rate of course. That can be very useful to see how hard you are working.
Find the setting that is easy to start but not too easy. You probably want to start out at 20-30% and see how that is...
I would probably pass on the 40 sec sprints I was refering too... They are very intense.
So start out at 20-25 minutes and add three minutes a week until you get to 40min. Increase intensity a little when things get to easy.
Intervals are the next step after a few weeks. Go for one minute high and three low. build up over time and enjoy your new machine!!!
Of course do not go any longer than your body lets you...
You are going to do great!