Much depends on exactly how you have defined your tables/relationships, but a single script can process the user selections to pull together a matching found set of records.
One General hint:
Make the fields on your "search layout" global fields (Click the storage tab under field options when you define the fields). The values in these fields will remain available to your script even after it enters find mode.
Your script might have this general format:
Go To Layout [Select a layout that refers to the table you want to search]
Enter find mode 
Set Field [YourTable::YourField; YourTable::GlobalSearchField]
#do such a set field step for each field you want to enter search criteria
Set Error capture [on]
Perform Find 
Set Error capture [off]
# set error capture prevents the Filemaker's "Records not found" dialog from interrupting the script if no records are found
If [get ( foundcount ) > 0 ]
Go to layout [Specify the layout from which you want to print]
#add any other steps here that you want for working with you new found set
Show Custom Dialog ["No records were found..."]
Thanks again Phil. I'll try that.
BTW, still working on my last FM issue (re. passwords). Spent a few hours on the phone with FIlemaker and Apple about it. There are still some other, systemic issues going on with the machine and it's been at the shop since Saturday but, so far, running a disk defragmenter appears to have resolved the issue with the one database opening without a password.
I appreciate your ongoing willingness to answer my questions.