Might be better off building a new one in the US and shipping it with your other stuff. Sales tax (import tax?) is pretty bad for electronics in the EU, stuff is a lot more expensive. Everything costs pretty much ~30% more.
You can package the computer in the box of the case and maybe take out the gpu and/or the cpu cooler and pack that separately so it doesn't break in shipping.
How much stuff are you bringing? Are you getting like a shipping container for furniture, etc. or just essentials? Are you staying in one spot for long? If not, gaming laptops might suit you better (once again, cheaper to buy in the US).