Now that I've had a 1/2 dozen or so flasks worth of seedlings to start I would say that the most important parameter to watch is air humidity and airflow.
I started my first couple of compots worth in my pleurothalid box indoors that has very consistent 70 to 80% humidity and fairly even temps (65 to 75), and lighting less than 1000fc. Under these conditions seedlings took off fairly well with little or no rot problems. After a few months I moved them to the greenhouse and they continue to grow very well.
However due to space limitations I tried starting some seedlings in the greenhouse where things are more variable. Generally the humidity is also high too, but light, temperature, and airflow are more varable depending on the spot.
I tried placing the seedlings near their respective parent plants and ended up with some very stressed seedlings and some losses. At that point I moved more established (1 month) seedlings out of the indoor box to make room for the newbies and they recovered well. The 1 month old compots now moved out to the GH have also done well since, but have them in a well shaded, and more consistently cool and humid spot.
Once they get to 6 months or so they are much more tolerant of adult plant conditions once acclimated.