A.N.
When mine got to that age where they wanted friend parties, I always limited the number to no more than the age they were turning (in your case, 6) however, it's your call.
How about a bowling party? Both my kids and their friends had a blast with that! Call a bowling alley to see what they offer - usually you can get a package deal that includes drinks and they should allow you to bring in cupcakes. With one, we did a lunch and ordered pizzas there, with the other, we just had an afternoon with cupcakes.
As far as the invites go, I would definitely avoid giving them out at school. You should be able to get addresses from the school to send them that way.