The need to pot up plants depends on the specific crop, your climate, and the variables of the particular season. Many crops can be germinated in shallow flats (plug trays, soil blocks, open flats) and then moved directly into the garden. Plants that may need to be potted up are typically long-season, heat-loving, and very cold-sensitive crops, such as tomatoes, peppers, and eggplant.
Standard nursery procedure is to germinate all crops in shallow flats, choose the healthiest individuals from each variety for potting up and graduate these to 4-inch pots or larger for continued indoor grow out. Almost any crop should be ready for outdoor planting directly from a 4-inch pot unless you start your crops incredibly early in the season, at which point potting up into gallon-size containers might be necessary or desired to hold them inside for a longer period without getting rootbound and stressed.
Use the following technique to grow the healthiest tomato and pepper plants!
A complete guide to growing cucumbers in your home garden.