Don't know about moving companies, I think it will be too expensive to move over furniture (from Kenosha), compared to buy it here! If it is a must, you would find companies for it, if you need to send some parcels, use UPS rather than US Mail, instead, maybe, organize a garage sale and use the cash to buy new.
Don't count on bring $ dollars here to exchange for ? euros. Don't bring any currency rather than ? Euros. You will have to open a bank account before start using your money, instead, bring your ATM card/s and make withdraws for immediate cash.
As far electrical items, here the voltage is different than in US, so read its labels, before you pack, you will need to buy, adapters for your plugs, coincidentally, I have two 220V -> 110V transformers that I brought, brand new, never used, PM me for details, they are quiet heavy though.
I flew over from Chicago via Dublin on AerLingus, better rates than anything else.
Thanks
Lorenzo