There are several acceptable positions to take after you drink the OO/GJ potion. What's most crucial is that you remain still for the 30+ minutes. I try to keep the position for at least 45 minutes, just to be safe.

Andreas Moritz's recommendation of lying on your back with your head raised on a couple of pillows (to put a slight pressure on the liver, to help squirt out all of those stones) is fairly easy to do and very comfortable, and maybe the most "natural". The other positions seem like doing yoga in bed. ;-)

Being able to be comfortable, relax and lie still is probably the most important part of the "post-drink meditation".

Both of the postions are good, depends on what you want. The opening of your stomach to your intestines is in the right side so lying on your right side will ensure that the mixture will vacate your stomach quickly. The function of the mixture is to go to the duodendum to make the GB contract. So for some people the quicker the better, then you get a good purge of bile that potentially brings a lot stuff with it. But for others, this might be a bit too strong as this forces the GB to contract very forcefully and this may result in nausea and getting the mixture back into your stomach. Not very nice and some people vomit as a result. However, the GB has contracted and the job is done so you might get good results nevertheless.

I have been lying on my back and on my right side and I can say that my experience backs up this description above. My advice would be that if you are afraid of being nauseous, lie on your back, if you want a strong contraction, lie on your right side. But, as always, every flush is different, so this may be just fine tuning. I am just sharing my understanding and experience, see what would work for you.