Veggie bed size and suggestions?

I'm building a bed for my fall vegetables this coming weekend. I've germinated everything so I just need a place for them now. I'd love some idea of how big to make the bed based on the following information:

• I will be planting purple broccoli (12 cells started), mixed lettuce (18 cells started), purple graffiti cauliflower (12 cells started), rainbow carrots (24 cells started) and dill (6 cells started)
• I am considering trying to keep the lettuce inside to keep it from bolting early but would it be ok outside in Northern VA (7a) heat until mature? I'm ok with early harvest as I have people who would love the food.
• Do the carrots need special soil? If so, is it such that I would need different soil for different parts of the bed if all of these are planted in the same bed?
• These seem like shade friendly plants for the most part, would they take damage in too much sun?

Thanks for any insight!