Depends on who is paying for your shipping? Are you?
Leave behind big electricals, we did bring our TV over (long since destroyed by a 2yo), and a converter to run it. Otherwise we put everything else into storage electrically wise, also all of the garage stuff is in storage, bbq, and a spare couch, mementoes, books/cds we didn't want to bring with us etc... It costs us about 70quid every 3mths for it throught White & Co, the company used to pay this, but we do at the moment.
How long are you coming for? Do you have DC? If it's less than 12mths, may not be worth it, but do bring things for the DC to make your home more familiar, duvet covers, pictures in their room etc... Always important for them to have their stuff, esp if they're young. But if the company is paying the shipping, just bring it. Have a GOOD clearout of stuff you don't use, and if time, sell off bits and pieces that are just taking up space. But think carefully about it, don't get rid of things for the sake of it, you may regret it later.
I don't think we got a reduction on our car insurance from previously good record, but you can bring that anyway, it's worth a try. We pay something like US2200 per year for 2 cars, one new, one about 5yo.
Your head will spin for the first week. OUr last move, DH took the first week off as we were in a hotel for 3 days then to an apartment, and we used it as a bit of a holiday/recce of the place. We drove all over to see where we might want to live and took the DC to the zoo, museums etc. to ease them in.