Talk to your local moving company, i.e. Redball, Viking, etc. Cost depends on how much you're shipping.
It is possible to pack up your own crate, then ship yourself, which is cheaper but a lot more work.
The movers will quote on the basis of standard size lift van usually (about 3'6" x 8' x 8' or 3'6" x 8' x 4' (half size) as I recall).
Although you're closer to VI, a full size lift van from CA (for example) runs about $3000, a second for $2000, etc. It may be two thirds of that from Chicago; but you need to get a quote.
Often, it doesn't make financial sense to ship furniture unless it's especially valuable, rare, or hard to replace sentimental pieces.
--T