Baby shampoo is great for cleaning make-up sponges and brushes, especially if you have sensitive skin; just a tiny squirt and wash them all in warm water. Sanitise them with a rinse in diluted disinfectant, then leave them to dry naturally. I use a cooling rack from the kitchen to let the air get all around.
washing machine is the way to go. However, regular detergent might leave residue and irritate your skin. I use silk and wool liquid by Persil but any baby safe detergent should do.