I find that the more durable things will last through the work week. On Sunday night I try to cut up broccoli florets, carrot and celery sticks and bell pepper strips. If I don't eat them all by Friday, the bell pepper strips would probably not be good any more, but the rest of them would still be edible as long as I started with fresh produce. I have some glass containers with airtight lids that I keep my cut veggies in. I shredded a cabbage up for 'slaw about two weeks ago and put it all in a Zip Lock bag, and it is still good - cabbage is very durable as long as it doesn't get exposed to moisture. Things like lettuce, it's best to cut up the day you want to use it. We usually just buy containers of baby greens because they don't require chopping, and are more nutritious than iceberg or Romaine lettuce anyway.
I'd say, try cutting up 3 days worth of stuff at first, and see how happy you are with the quality of the cut produce on day 3. Some of us are pickier than others. You could also pick up something called Fruit Fresh that you sprinkle on things like sliced apples to keep them from browning. It is usually sold with the canning supplies most supermarkets carry this time of year. You can also get the same effect by dunking your sliced fruit in a bit of lemon juice mixed with water.