If you mean design the website, code it, create the database, create a secure socket for transmission of private data, etc, then unless you have an extensive background in development, I would say definitely not. You think it is expensive setting up a store, wait until the lawsuit you get from allowing private data to be compromised.
At a minimum, you are going to want someone else to handle and store the data (which makes it their responsibility to keep the data secure). You could do it yourself with any of a number of freely available packages, but there will be some overhead to get you up and running.
The first question is to determine what your needs really are. Do you need to store customer data at all? If not, then you can probably safely do it yourself. It just depends.