We brought all our furniture and white goods (except dishwasher which was built in), which worked for us. The container was expensive (40' cube) but for the cost of it, we would not have been able to buy all the stuff inside, if you see what I mean! The house we rented and the house we bought both had dishwasher in. Here it's a Fisher & Paykel Dishdrawer, which is fine.
I don't miss any particular products: here I use Persil Low Suds powder for my front loader - everything else causes a flood!- whilst I used to use Ariel tabs in UK; Finish tabs are replaced here by Active Dishwasher powder which we find really good.
I buy shampoo etc here without really thinking about comparing to UK. Anyway, after nearly 18 months, I can hardly remember what we used over there!
Being the type of person who is not attached to any particular brands, I couldn't be bothered to bring supplies of toiletries/cleaning stuff with me and as I said, we find everything here to be fine. Don't know if I'm odd, but I always thought toiletries etc were dear in UK too!
Gil