I've hatched using both methods. However, I've had more success with higher hatch rates by standing them up. You can use the bottom of an egg carton with a hole punched in the bottom of each depression so water can drain out just in case it gets in. You'll still need to turn the eggs. To do so, you can simply tilt the incubator at an angle and alternate that angle 3-4 times a day.
If you lay them down on their side, mark opposite sides with something like an "X" and an "O". You'll have to turn each egg individually by hand, which takes longer and you'll have to keep the incubator open for a longer period of time.
Another thing I like to do is write the date I set the eggs on the top of the egg. That way you'll know what day they were set and then can look up the day they are due to hatch easier. I learned to do this after forgetting to write down when I had set eggs on my calender several times.