Double row planting allows you to space a bit wider. I would space 3' and the row behind is offset so that the arborvitae of the second row are in the middle of that 3' space. The second row should be 3' from the first row. You will have equilateral triangles with every 3 arborvitae. Each arborvitae will be 3' away from its neighbors, side and back and front. Do not skimp with space. 3' is truly minimum between arborvitae hedges.
Doing this you will have healthier arborvitae, less shading and die off between the shrubs and faster growth. Another very cool thing is if one dies (for reasons other than Phytophthora explained later) it will hardly be noticeable. Water well the first year. Not soggy but keep moist. Try not to water overhead.
Are your plants B & B or are they in pots? How large of a pot? Allow your shrubs to acclimate to their new home before any fertilizer. A soil test will help and ask for phytophthora count if available. This disease is one you do not want.
If you see a branch or two die to be followed by the death of the entire shrub...you might have Phytophthora or had Phytophthora then you have to remove that shrub and ask us how to proceed. The entire hedge could easily die from this fungus...well, it is akin to fungus. This is on the rare side but all of the arborviatae hedges that I know that had problems it was always Phytophthora. Check out this article to protect your investment. Have you already purchased your arborvitae? Find out from the nursery what they warranty. This article helps you to be able to LOOK at nursery stock to suss out stuff you DON'T want. Most Phytophthora comes with nursery stock. Be a pain, be a know it all about Phtophthora. Get your soil test from your closest University Cooperative Extension Service. Cheap and worth it. I doubt they'll be able to check for Phytophthora but if you were able to prove you had no phytopohthora in your soil and you got it from the nursery and they knew you were concerned about this disease they would have to replace those shrubs. Phytophthora woody perennials.
Have you ever had a tree or shrub die completely, starting as a 'flag' (a very dead branch among healthy looking foliage and progressing to total kill? If so do not use arborvitae as your hedge. There are many other solutions. Many better choices for hedges. Check for variety resistance. Ask about resistance of the shrub you want to purchase. Check out the nursery's warranty. Are you having a subcontractor or contractor purchasing and planting? Check out their licenses, their bonding and THEIR warranty. Let them know you KNOW about this disease.
Get a soil test, get to know your Cooperative Extension Service, the Master Gardeners, Arborists by NAME. Valuable! This hedge will not be cheap. How long is your screen to be? (don't prune until the height is attained that you expect and always use alcohol to clean your blades). How much room widthwise do you have? Will this be on neighbor's property? Get an informal yet written agreement between you and your neighbor if so! I've been involved in many civil suits between neighbors and trust me you do not want that to happen. Communicate with your neighbor closely.
Your neighbor could also have this fungus in their soil that will infect and kill your hedge. This fungus doesn't affect all genus and species of plants. Arborvitae happens to be very susceptible, however. Try to get RESISTANT strains or variety of arborvitae.
Learn the nursery's history about shrub, tree death. Are they even aware of Phytophthora? Very unfortunate to go to court over this type of thing. Just trying to get you to prepare JUST IN CASE. Please ask more questions when you get further into this project. I hate to see neighbors sue each other or have to sue your Nursery. The more you communicate, the less the chance of problems and court stuff.
Hope not to scare you but just record everything including dates/conversations that surround the purchase and installation of your hedge, know more about your nursery stock before purchase, the nursery, warranties, a soil test...and with this you'll have your 'ducks' in a row be able to succeed in court. Better yet, communicating this knowledge you will lessen any problems and protect your investment. And your relationship with neighbors and nursery.
Most of the court problems I was asked to expert were about arborvitae hedges! A few with big trees and limbs crossing the property lines but amazing the time spent in court over arborvitae hedges...so I am giving you a bit more information that you thought but I sure hated dealing with that EXPENSIVE drama!