Hi, Deborah.
I have no experience with international adoption as we have opted to go the domestic route since we would like to parent a newborn and have an open relationship with the birth parents. Perhaps the other moderator, Jessica, will be able to chime in with some helpful hints for you.
But in the meantime.... have you chosen an agency yet? If not, and Hungary is your only target country you may want to investigate several agencies that facilitate adoptions in that country and compare their fees, policies, placement rates, waiting times, etc. before you sign a contract to work with them.
I really feel from reading many posts on these boards about the process, that going it alone, or even with just an attorney, in the endeavor to adopt internationally would be overwhelming to say the least! Each country's legalities are going to differ, and to bring your child home, all the i's have to be dotted and the t's crossed exactly the right way. Plus there is the matter of the home study which I understand has to be written up just so for each country you want to adopt from. You have much paperwork ahead of you, don't despair, the first step is the hardest one. Just find an agency and get started!