Well, there are a few ways to access your PC files remotely using Internet. A few of them have been explained here.
It Is one of the trustworthy means of accessing your PC remotely. It Is available on Linux, Mac and Windows. They also have apps for Android and iOS. But the mobile apps work for transferring files from your remote PC.
There are a couple of Remote Desktop utilities available, yet TeamViewer has been treated as the most trustworthy of them all.
2. FTP servers
You can set up FTP server for your PC and grant Internet access to it. However, this method exposes your PC to security threats. Your PC needs to be in a switched on condition always for this to work.
3. Use network attached storage
You can use the NAS or Network Attached Storage devices. Most of them have support for accessing the files over the Internet. But, they are most insecure way of making your files available on the Internet. You may also connect a USB drive to the port on your router if it supports one. This drive will be accessible on your LAN.
4. Use VPNs
This is one of safest and secure ways to connect your PC to Internet and access it remotely. You will need to set up a VPN server on your home network and now, your PC will be a part of your LAN. You can access the local storage of your PC remotely.
Live....and Let Live!