Don't ask many children.
Don't do complicated food. Imagine how many sandwiches DD would eat, multiply by the number of children, then halve it. You will still have too many. What children actually eat at parties is Hula Hoops (one sharing bag), a few cocktail sausages, a few grapes and blueberries, and the cake/biscuits. Maltesers are good too. Catered for a tenner and minimal effort.
Complicated paper plates are pretty but if you have the same rainbow IKEA plastic plates and beakers as everyone else they do just as well. Otherwise pound shops usually have the party plates/cups/napkins etc.
Don't do party bags - they quickly add up to stupid money. Instead get a multipack of books from eg the Book People and wrap them in tissue paper. Each child takes a balloon, a book and a wrapped up cake home.
If you're a good baker, would you consider a short baking session? Roll out and cut out biscuit shapes early on, bake while they run around like mad things, then a couple of colours of thickish water icing and a few raisins and hundreds and thousands on top?
At three most if not all parents will stay. Offer tea/coffee and a plate of home made scones with a wee dollop of jam. Feels very indulgent for the adults but is cheap and easy for you.
Three year olds love dancing. A couple of rounds of musical bumps tires them out. If they all go to nursery/preschool/toddler groups then you could have a singsong too - each child in turn choosing their favourite song.