Shipping your belongings over to the U.A.E. might not be more expensive than re-buying everything, especially when you consider that reserving a cargo container will help you take along your "rare items" (those of bullet point #1). In order to find out about the total cost of the shipping, you can contact an international movers company (google these terms and your current city, and you will find a lot of options). Usually these people will coordinate the full move for you, and they can even pack your things! Obviously it will be rather expensive. Another cheaper option is to split the work between different companies : 

• one that will pick up your things (you could do it yourself with a truck and a couple of friends if you leave in a coastal city that has a big port). Typically, it's a traditional moving company
• one that will send your things over to Abu Dhabi by boat (they're called freight forwarders)
• one that will take care of the custom's clearance in Abu Dhabi (it's a really big deal, so don't forget this step!!), store your belongings if your home isn't ready, and will deliver them to you

Depending on your location, there might not be a million boats going to Abu Dhabi every day. This is pretty obvious, but plan your move ahead of time so you don't get screwed by the deadlines. Also, note that your belongings will have to be delivered to the freight forwarder at least one week prior to the departure of the boat : your things need to be loaded in the container, and then the boat has to be loaded with all the containers that will travel with yours. 

The freight forwarder will tell you to prepare a packing list for customs clearance purposes, don't be surprised. Basically, you will have to list of all your items: each of your box will be numbered and you will have to indicate what is in every box. It is a little tedious, but it is actually pretty helpful when you unpack (if you kept a copy of the packing list!). Additionally, you will need to pack all of your books, pictures, CDs, artworks and such in boxes separated from the other items. Indeed, these are the things that will be inspected in priority by the customs agents in Abu Dhabi. You can't have anything that promotes crime or drugs, that has a pornographic nature, nor that is offensive to Islam. 

The freight forwarder will also let you know how long the shipping will take. It is pretty long (as in several weeks), which means that you may have your apartment before your furniture. Yes, I know, it's a pain, but again, it really depends on your personal preferences and how attached you are to your belongings. After the shipment reaches Abu Dhabi, your container will be inspected by customs and this process can take another several weeks. It really depends on their workload, and how many things you have I guess.
Another point that I think is worth mentioning is that the electricity voltage is probably different in Abu Dhabi than in your home country. Since I don't understand anything (and am not particularly interested in) to electricity issues, I recommend this website that does a nice summary. My point is that if you export your electric items (TV, hair dryer, depilator, video games, computer, etc), you will need to make sure that you have the correct adapters and converters before plugging them in! Otherwise, your stuff will not work, or worse, the Abu Dhabi power could fry them! It happened to my hair dryer, and worse, to a friend's HP computer :-(

So, what do you think? Ready to pack?

UPDATE 17/07/2012
I finally received my container last week : yes, this is the option that I chose! :-)
Here are a few additional tips so you don't make the same mistakes as me :

• Put a few little bottles of water in the fridge so you can offer cold water at the end of the delivery. It doesn't cost you anything, and it will be greatly appreciated. These guys work in the warmth all day, and sometimes I get really concerned about them staying hydrated. 
• Use your packing list to check that all the items are delivered. If some boxes are missing, don't sign anything and call the moving company right away.
• I highly suggest you decluter one room after the other. It might seem like common sense, but you will find yourself with a terrible mess everywhere faster than you think if you don't do that. I chose to organize my bedroom first, so I'd have a decent place to sleep at night. And by decent I mean no boxes everywhere, no dust, clean sheets, etc.
• Ikea furnitures don't like being moved around. I can testify :-D
• Electric items don't do well. It might really be cheaper to buy new hairdryers and small kitchen appliances (blender, electric kettle, etc) than to buy power converters. Really. 
• Since the container will be on the boat, which will be on the sea, for several weeks, it is a safe bet that there will be humidity inside your container... Here is what some of my boxes looked like after unpacking (and drying for a few days in my apartment - yes, the bottom of the bow is still wet...) : 

•  If you have a few humidity absorbers (such as Rubson's), put them in the container. Now I really understand why shoes and purses made in China have these little humidity-absorbing baggies inside... I learned it the hard way :( 
• Another really important tip is to pack your clothes, shoes, particularly those in non synthetic materials, inside big plastic covers (that close with a zip), and then box them. I assure you, 80% of my clothes arrived with mold on them or a terrible smell, so I had to spend 3 days doing laundry non stop. In any case, make sure you have some detergent and color-friendly bleach ready. Leather shoes and jackets can be cleaned of their mold with rubbing alcohol.
• Crafters and artists, same rule will apply to your supplies. Paper, canvas, etc are very prone to mold. I had to throw away all my collection of scrapbooking papers :-(