A good place for factual information is the adoption website of the U.S. State Department, at adoption.state.gov. When you are on that site, find the drop-down box of country information on the right side of the page, and click on "Poland" or "Ukraine". When you get to the right page, click on the box marked "Expand All", and you will see information about the characteristics of the available children, the requirements for parents, the timetable, the process, and so on. You will also learn whether a country has ratified the Hague Convention on international adoption, or not, because that will tell you which form you need to use to get preliminary USCIS approval of your fitness to bring a child to the U.S.
Do be aware that, with Ukraine, children under age six are almost never adoptable. In fact, if you submit a dossier that approves you only for healthy children under age six, it may be returned to you by Ukraine's government. If you are open to children with moderate special needs, you may be able to adopt a younger child. Be aware that Ukraine is committed to finding homes for children with moderate to severe special needs, and for older school aged children, who are least likely to find homes domestically. While not all parents have this experience, at least some families who travel to identify children from books kept in a Ukrainian government office report being shown, at least at first, only books containing children with severe or multiple special needs.
When you first travel to go through books of adoptable children in a Ukrainian government office, you will not be allowed to have a private agency representative, facilitator, or translator accompany you; Ukraine will provide a translator. Once you have identified some children to meet, and are traveling around Poland to meet them, you may bring an agency representative, facilitator, or translator with you. If you don't find a child in the books or on visits, you are welcome to go home and wait for Ukraine to grant you another chance to find and adopt a child. You may make up to three visits. Remember that, when you get to an orphanage, if you don't feel that you can parent the child you selected at the Ukrainian government office, you will NOT be shown other children from that orphanage, and will not be permitted to request a child whom you may meet while touring the facility.
With regard to Poland, be aware that one of the three social welfare organizations allowed to place children with adoptive parents in the U.S. will accept only Catholic families. Also, there tends to be a strong preference for families of Polish heritage. In addition, be aware that most of the children have been removed from their biological families by the government, for reasons such as abuse or neglect; there are few voluntary relinquishments. This may affect the emotional wellbeing of the adoptable children. In addition, you will have a better chance of being referred a young child if you are open to special needs, as children with special needs are less likely to find homes domestically. Unlike with Ukraine, you will get a referral prior to travel, so you will have time to let an adoption medicine specialist review referral documents to see if there are any obvious conditions that you may not feel comfortable accepting, and to investigate resources available in your community to meet a child's needs.