I would suggest getting a twin leg stand as it keeps the bike completely upright as you put the child in the seat. On level ground the stand is quite capable of keeping the bike upright with the child on board. However, it's not stable enough to keep upright if they decide to start throwing their weight around (well, depending on the weight of the child), so you always need to be physically beside the bike in case the child manages to topple it. As far as I remember though my son only managed to start the bike toppling once and of course I was on hand to stop it.
The one I got for my bike (and I love it so much I've kept it on, even though my son is now too big to go on the back of my bike) is the Pletscher twin leg prop stand. I did try the Hebie one but I found that my heels would clip it when it was retracted so I had to return it. Mind you, I have size 12 feet.
One of the really nice things about having a twin leg stand is that you can use it as a budget workstand - the bike is balanced so that it rests on the front wheel and the stand when there's nothing on the back, so I can adjust my gears / brake etc anywhere there's a bit of flat ground. If I need to do something to the rear wheel, I just clip my pannier on to the back.
