Hi Keith,
You can certainily have a single page and form for each of those requests using one field. Something like this:
Please select your interests:
Product Demo
Health check of a certain application
Then create separate smart campaigns triggers to send them down the different workflows based on selection.
In terms of creating a new field in SFDC and/or just Marketo, it all depends on if you need that data in SFDC or not. If the data isn't needed in SFDC, then you can create a custom field in Marketo.
Hope this helps!