That would be, as you suspect, "totally straightforward"—
1. make your PRINT field a number field. In the Data Inspector, set this field as checkbox set, with the single value 1 (create that as a value list—see screenshot).
2. for a nice effect, resize the field to show only the checkbox, not the 1 beside it. Now, whenever this checkbox is selected it will either add or remove the value 1 from the field.
3. make the first step of your Print script Perform Find, and find any records with 1 in the PRINT field.
4. once the records you wish to print are checked, run your script.
Thank you much for the reply - that did the trick! I realize I got caught up thinking like a web programmer in that you have to parse the data from a webpage before you can manipulate it. Filemaker makes it MUCH easier by storing your entries as you move from field to field. This was a much simpler solution than I realized.