Moving from US to Dammam

It's good advice for him to settle before you arrive. He should expect is Iqama, bank account, driver's license process to take a couple of somewhat frustrating months, so waiting 2-3 months before you follow is a worthwhile approach.

Get a good carryon roller suitcase. There are differences in sizes between US and international overhead bins, the international ones are smaller.
When I flew over on Emirates my carry on was too large for the coach bins, but it's fine on KLM/Delta. Having a change of clothes or two should be considered a must with your carryon in case your luggage is delayed. I had that happen on my flight over and after 30+ hours of flying, you'll want a clean change of clothes!

24 gallon Rubbermaid action packers have been my preferred means of packing stuff on airlines, much more convenient size than a suitcase and less expensive. Yes Costco has less expensive tubs that are slightly larger, but you will be charged oversized luggage fees (way more than the price difference in the tubs), and they aren't as durable so you aren't saving anything. Some people use cardboard movers boxes, the airlines can be real gorillas so I'd suggest the action packers over cardboard as the boxes are pretty much single use and disposable. The action packers can be used to store stuff, for organizing camping gear or the stuff you bring for a day at the beach, etc. Also put a strap around the lid and through the buckles. Cargo straps you can pick up as four packs work great, ratchet straps are overkill but again they can come in handy if you get into camping. TSA will rifle through your box's so provide a re-usable means of closing them up and keeping them closed during transport.

Duffle bags are also great luggage as when you return home on your expats you can stuff a couple of them in a nearly empty suitcase and have them to bring back items from home. On my return trips I usually bring an action packer with my clothes and a couple duffle bags in it.

A bicycle is really handy for getting around camp before you get a car so I'd highly recommend brining one. You can get a cardboard bike box from a bike store for $5-10, sometimes they will give them to you for free. They are also convenient for shipping longer items like fishing rods, tennis rackets, etc.

Being based in Dhahran you can buy most anything you want in Khobar and it's a $10 cab ride so I wouldn't go crazy with what you bring. But the first few weeks the jet lag really clobbers you so you likely won't want to be shopping too much. Your house will most likely be wired 220V, so it's best to just purchase the appliances you need locally. A couple of power converters and appropriate plugs for dual voltage items like computer power supplies and phone chargers are worth bringing. The plugs are a British plug.

If you have any hobbies or sports you enjoy, plan to bring that gear with you as those sorts of items are limited and generally lower quality in the kingdom. For home items, I would just plan to purchase locally. I'm in Udhailiyah and have an old house with no 220V sockets so had to bring all my 110V appliances. I would not have brought any of those if I had a 220V house.

If you have favorite spice mixes or sauces, you might want to bring some. If you have a vacuum packer vacuum bagging them will protect them from spilling in your luggage. You can pretty much get any spices you can imagine and quite a few you've likely never heard of our used in the super markets. Nutmeg is something you can't find as there is some restriction in the kingdom but I don't think you'd have any problem brining in a spice jar.

If you have more specific questions, send me a PM. I don't check this forum that often so it might be a week or two before I reply.