That is what Back-to-My-Mac is going to give you. And to a certain extent TeamViewer.
Back-to-My-Mac allows you to Screen Share into your remote Mac and do anything there that you can do sitting at the remote Mac's keyboard except plug and unplug things.
Back-to-My-Mac will allow you to mount your remote Mac's file system and access it as a network storage device on the Mac you have with you.
Back-to-My-Mac should make your remote Mac appear as a clickable item in your Finder side-bar.
Back-to-My-Mac does NOT require any additional software. Everything you need is already in your 2 Macs.
TeamViewer (you do have to install it on both systems, and configure the remote system to accept unattended connections). Anyway, TeamViewer will allow you to access your remote Mac's screen and do anything remotely that you could do sitting that the remote Mac (again, except plug and unplug things).
TeamViewer has a way to transfer files between the 2 systems. It is not file sharing, so you could not access that remote files via one of your apps, but you could transfer the file to your local Mac and then access the duplicate local copy from your app.
TeamViewer is cross platform, and can be used on a Windows PC to access your Remote Mac. A Linux TeamViewer version is also available).
Both of these utilities are very good at doing remote Mac access. And they are about as easy as you are going to get.
I strongly suggest you look at Back-to-My-Mac first, as suggested by Duane
You can also contact any Apple Store and ask them for help in setting up Back-to-My-Mac.