The best rule to live by is the Golden Rule, I believe. Treat others as you wish to be treated. It's hard for a lot of people to see just how effective that rule is, but I try to live by it as much as I possibly can. In fact the Golden Rule covers a lot of things by itself: lying, leaving a mess, being polite, helping each other, asking permission, and much more. I would still spell things out for the kids though.
Other rules I would post in my house:
-be polite and respectful to one another
-offer help to each other
-When you're done with something, it goes back where it belongs [not just toys, but especially toys! This can apply to books, backpacks, shoes, laundry, dishes, the cordless phone, etc]
-I agree with the previous poster- If you can't say something nice, don't say anything at all. It would be better if it was reworded "if you can't say something respectfully, don't say anything at all" because sometimes the truth needs to be told and it may not be nice...like if someone decides to do a really crazy hairdo and it is just not right and something needs to be said- in a respectful way- NOT "oh my god what is wrong with your hair?!". however respect is a tough concept to grasp for kids so for now you could stick with the original.
-Tell the truth
-No dessert if you don't eat your veggies and drink your milk. It really is a great rule.
-Bed time is at ______. This one may be different for each kid and may change over time but it's good to have it posted as a rule to remind them, and to remind you to stick to it if you're letting them stay up too late at times
-Making a chore chart to go alongside the other rules would be good...I think because of their age you could have them stick to the same things each week. The 3 year old can make his bed, sort his clothes and put them in his dresser, take out any garbage from smaller trash cans in the house like from the bathrooms, and work alongside you with other chores. The 9 year old can pretty much do everything but maybe not quite ready to do the dishes completely...so you would have to pick a couple that you think she can handle weekly.
-Ask permission before borrowing something
-If you have hurt someone in any way, even if by accident, apologize AND make up for it.
-Everyone has a right to their own opinions.
-Homework is done first
-We will all have a meal together around a table _____times a week. This will probably change a lot, and I would suggest posting a "family meal schedule" every week or every two weeks and make no exceptions. Family is the first priority. As the mom you know everything that is going on and what's happening on what days so you would have to plan it carefully to have success. Obviously it would be good if it was every meal but with different schedules and as the kids get older and are in sports and other activities and when they get to be teenagers it will be much more difficult. It's still so important though
That's all I can think of right now but I will be watching for the responses! I need to make a list too