You don't need to put it on DMZ or open up file sharing to make ftp work. As stated above, the only thing you have to be sure of is that port 21 (assuming that the ftp server is running on standard port - 21) in the ftp server is open. This setup will work fine and you can transfer files internally (inside your linksys).
Now, if you want to access the ftp server from *outside* of your router (i.e anywhere on the internet, dial-up, other cable connection, etc), the next step is to make sure you have port forwarding on your linksys router from port 21, and forward it to the internal IP address of the ftp server (this is something like 192.168.xxx.xxx or 10.4.xxx.xxx). Of course, you need to know your 'outside' IP address (the IP address from your ISP, which is now the IP address of your linksys router), but I'm sure you already know about this.
The last thing that is most likely to cause a problem is that your ISP might simply block port 21 because they don't allow you to host an ftp server on your connection. Some ISPs block certain ports like 80 and 21 to make sure you don't host a website or an ftp server from home. The only way around this is to host the ftp server on other port number that is not blocked. The catch is that the ftp client who connect to it must also know about it and specify which port they want to connect to.