I do as Moyn does with the lettuces, I wash and spin dry the leaves and lay out
three or 4 paper towels still connected, place the leaves on them and roll them up. They keep for quite a while, depending on where they came from. Radishes I cut all but a half inch of tops off and wash and put in plastic bags. I re-wash and trim as I use them. They seem to stay fresher that way. Vegetables such as broccoli, corn, green beans, cauliflower, beets, peppers, green onions, carrots, celery, etc are washed and trimmed as needed.
I've been buying parsley and cilantro with the roots on and find they keep for a long time if put in a vase or glass with water, covered with a plastic bag and refrigerated. I snap the ends from asparagus and stand them in a container with a little water, cover with a plastic bag and use quickly. Interestingly, watercress keeps best if turned upside down and the leaves are immersed in water.
I know what you mean about it being tedious, I spend a couple hours doing it on Saturday after I go to the farmers market or organic farm stand, but salad making is much simpler.