some quick info:
If you bring household goods, there really aren't many ways to get them here. From the US, Eimskip's the big cargo ship company, from Europe there is Eimskip, Samskip, and I've heard there's a German line that operates occasionally too.
Furniture here is (relatively) expensive, even a lot of the second hand goods, so I know plenty of people who've brought their household goods here and found it cost-effective. If you're moving from America, your electronic appliances will not work without adapters and converters. For items like computers with dual voltage, it's no problem, but coffee machines, lamps, and the like are best not brought. If you're coming from Europe it's probably more cost effective to bring those with you. Washing machines, refrigerators, espresso machines, all very expensive here.
bedding and other household linen can be purchased inexpensively here at places like IKEA and rumfatalagerinn so it's not needed to bring with you.
one note: if you're bringing equipment for horse riding or for fishing, it must be disinfected and have a certificate to prove that it was done.
regarding fodostuffs, I'm not aware of anything specifically banned, so I'd guess that the rules applying to what you can bring when flying into Iceland probably apply. Info on that is here:
when I moved I brought some of my favorite household and things I knew I couldn't buy in Iceland (namely my handweaving loom and weaving fibers that aren't available here). It's nice to have my artwork and a few heirloom pieces with me.