Although not a wonderful sleeping position for everyone, sleeping flat on your back or with a pillow under your knees will put the least amount of pressure on your abdomen.
If you do need to move to keep from getting stiff you might find that placing a pillow under your right side might help (this puts the right side slightly elevated). If it’s done the other direction it can sometimes put more pressure on the lower right quadrant which is what you want to avoid.
If your surgery was a laparoscopy without complications you’ll likely feel better within 2 weeks although some people will be sore for longer. Always stay in contact with your doctor if you have knew or persistent pain that isn’t healing. In rare cases the stump of the appendix that is left behind can become inflamed will mimic all of the effects of full blown appendicitis (which is exactly what it is, just on the stump).