We entertain often. Saturday is definitely better for most people. Parties on Sundays sometimes conflict with church service.
I agree with the last poster...something simple like a BBQ will be great. Those are easy to put together and relatively inexpensive and you don't have to worry about a kid menu. I would just out a start time on the invite...most parties wind themselves down after two or three hours. (The last house warming we went to hey had a fajita bar. They grilled the meat and then you put together your own fajitas with the toppings they had prepared. It was fun. They served margaritas and beer with it. )
For a house warming I wouldn't worry about any games, just plan on walking small groups through so they can check out your house.
And you need to decide if kids are welcome, if not, be specific on your invitation. Most of our parties are kid friendly. It makes for a better turn out when parents don't have to find a sitter. I have discovered that bubbles and bubble wands from the dollar store are about all the entertainment necessary for little ones. They can make that fun last hours, just make sure you have plenty. The less they have to share, the less arguing there will be.
Many people bring house warming gifts, so you may need to make time to open those.
Hope this helps!
Have fun!
Congrats on the new home.