Shipping services to Hungary
You can ship to Hungary via ocean freight, land freight, cargo holds or even through a courier service. The least expensive way will generally be the slowest mode of travel but that may not be conducive to what you are trying to ship there. COD and Certified mail is not generally offered to Hungary but you can inquire when you are ready to ship as some shipping company may have added that service.
Customs in Hungary
Generally speaking, you will want your declared value of any parcel sent to Hungary to be valued at under $2,499. If it is over that amount, you will be charged some fairly hefty fees. If possible consider splitting your shipment into two or three smaller shipments to keep it under this value threshold. You should have the PS 2976 form filled out with each shipment for the Customs office as well as have a bill of lading and a certificate of origin. Copies of these forms are available at the various shipping companies as well as you can find them on line. You should expect your package to be held up in the Customs office for a minimal amount of time, assuming you have all your paperwork in order and you either pre pay for the duty fees when applicable or pay them promptly upon hearing of them. Not paying the Customs fees can result in either your package being seized by the department or possibly even returned to the sender in some cases.
Shipping limitations to Hungary
You are not allowed to ship any sort of currency (coins, bank notes, traveler's checks, or currency notes) unless you sent through an insured means. And even then it can be dicey. Your shipping company will be able to advise you on the best way to ship such things so you will want to check with them. You also can not send any radioactive materials, but most everything else can and will be accepted there, assuming the duty is paid on the parcel when applicable.