Encryption of .csv files

Encryption of .csv files

I'm working for a client who is collecting sensitive data from clients via
Wufoo forms embedded on their website. They have dozens of unique forms
and for simplicity, I have written a script with the API to grab all the
data simultaneously and output it as .csv files on their server.
A concern has been raised about the security of this information. Wufoo
encrypts all of their data with 128 bit SSL, but once the data leaves
Wufoo's servers, the responsibility is on me to make sure it's still
secure.
I've never worked with any kind of secure information and really have no
idea where to start in this process. I'm looking for any kind of advice,
or to be pointed in the direction of further information on this topic.
Ideally, the process of collecting and outputting data would function the
same, just in a more secure way, but maybe this requires an entire
reworking of the system? Again, any advice is appreciated.