Maybe there is no way to request a specific file type but what is the best way to request a file (paper or digital) that can be converted easiestly?
A common strategy used by journalists I've worked with is to first FOIA a data schema or other explanation of how the data is managed by the government body. This allows you to be much more explicit in constructing your actual request.
And as rcackerman noted, you may not actually have to start with a FOIA -- but ask them what they have and how they have it, so that when you do file a FOIA for actual data, you can be precise.
In general, it is good to have a sense of the most common ways machine-readable data is available (eg, API access, CSV/Excel, etc). With this knowledge, make a phone call to the appropriate government official and chat with them about what they have available. Verbally ask them if they have specific formats, or if they have a database (and if so, can they dump the contents into a CSV file, for instance). With this questioning they will usually (though not always) indicate what they have and how you can get it, then you can tailor the language of your written request accordingly.
Getting on the phone for a few minutes before sending a written request can save you a lot of back-and-forth and needless delays. It will also give your request more personality and presence, and therefore quicker fulfillment.
If you still need help, a great resource to help you most effectively craft a FOIA request -- for machine-readable data or otherwise -- would be MuckRock.com. The director, Michael Morisy, is very approachable and always happy to help. You can email him at Michael@MuckRock.com
More about MuckRock:
MuckRock acts as a request proxy, e-mailing, faxing or even snail mailing the request on your behalf. Documents are sent to our offices to be prepared by our team of experts for your convenience. We can even assist with analyzing your data. Our intuitive system ensures that your documents are for your eyes only until you're ready to publish.
Summarizing from a thread on NICAR-L,
Many reporters found that is was helpful to include technical terms in request, like "ASCII text", "manipulatable digital format", "Excel, CSV or other delimited text or spreadsheet format".
The journalists seemed to think this helped because such a request would be more likely routed to someone who understood how the data was stored and knew what you were asking for.
Simply asking for the data in "Electronic Format" was considered a bad idea, since PDFs are an "Electronic Format".
Look at this question about official/unofficial data requests. Similarly, I've found it useful to ask questions about what data (or maybe just paper files) exist so you can ask for exactly what you want.
Perhaps asking for the data in a machine-readable format like X, Y, or Z and expressly requesting it not be in PDF.
(Disclaimer - I am the Sr. API Strategist for GSA)
In the United Kingdom the law is currently being changed to provide a 'Right to Data' as part of the Freedom of Information legislation, so if requesting from a UK Authority then it may be useful to reference the draft Code of Practice (datasets) which states that an authority 'Disclose datasets in an electronic form which is capable of re-use'.