Washing and dealing with bedding can take a lot of time. To simplify things around here, we do the following:
1. Except for my oldest daughter, age 9, we only use fitted sheets and mattress pads plus blankets on our children's beds. It simplifies daily bed-making considerably, as all that's needed is to either spread the blanket over the bed or fold it and place it at the foot of the bed. It also takes up a lot less room in the washer to wash a child-sized quilt or blanket rather than a bulky comforter.
2. We wrap our mattresses like a cocoon, with layer after layer of waterproof mattress pad and fitted sheets. I stocked up on washable waterproof mattress pads last time they were 60% off at Shopko (make sure you buy the washable kind; I've had some that fell apart in the dryer, even on low heat), and recently bought lots of nice fitted sheets for $1.99. On one son's bed right now, I have 5 layers!
This way, when it's time to wash the sheets, I only have to peel off one fitted sheet and one pad to wash, leaving a new set underneath clean and ready to go. Believe me, when a child throws up in the middle of the night, the last thing you want to do is tussle around putting new sheets on their bed.
One mom I know swears by buying only white sheets for all her beds so that she can bleach them and make them last longer, but I've yet to try that tip!