The method to use depends on the quantity of emails and the nature of it content.
The general procedure will be:
1. Extract the email from the Email Server/inbox.
2. Define the structure of the fields (in case you opted for RDBMS).
3. Load the different part of the email in the different fields.
4. Apply your analytics tools/algorithms.
There are ton of open sources programs/databases to use.
But, if this is small experiment on a small number of observations (emails); I can recommended you to use SAP IQ (there is a demo that you can download from SAP web site), Python (to implement your algorithms, but you can use R or SAS or any tool of your choice), and Tableaux for your front end.
Please note that this can also accomplished with other non RDBMS tools, like HADOOP.