Access Mac mini remotely (Screen Sharing + File System)
You need to configure port-forwarding on your Time Capsule.  Since your ISP doesn't give you a static IP address, then you will need a dynamic-DNS service to resolve your home's IP address to a URL which you will use when you're away from home to connect to your Mac Mini.  You'll also need to configure your Time Capsule to handle Wake-On-LAN/Wake-On-Demand packets.  In the bullet points below I've listed the basic requirements and included links to step-by-step instructions for each step.  


You need a static IP address from your ISP or a dynamic DNS service like dyndns.com to resolve a changing IP address from a URL which you can choose.
You need to setup Wake-On-Demand as described by Apple on your Time Capsule
Finally, you need to forward ports on your Time Capsule to your Mac Mini so that incoming connections from your client software when you're away from home can reach your Mac Mini.