You are describing two distinct approaches and both can be made to work in FileMaker.
You can list records in a list view or in a portal and make the field or group of fields in the row a button. The button can perform a script that assigns the value to a field in your current record. Here's one possible script:
Set Variable [$ID ; value: YourPickListTable::PrimaryKeyField ]
Go To Layout [//specify original layout ]
Set Field [YourTable::ForeignKeyField ; $ID]
This assumes a separate layout for your pick list, if you display the list in a portal on the same layout, you don't even need the go to layout step. You can also pop up a floating window for this and then you'd close the window after setting the variable.
Drop Down List:
You can specify value lists that use the "use values from field" option to list values drawn from a table in your system. If you use the show only related values option this list of values can be limited to only those that match a specified criteria. This last method is called a conditional value list.