To put how old and out dated the hardware in your Mac Mini is into perspective, the GPU doesn't even support 4k monitors. i.e. you can't even watch 4k content on it, so editing it is simply beyond it's capabilities.
It was slow and and at low end of the performance spectrum when it was new, while the processor is 6 years out of date, it's built off of technology that is 9 years out of date.
It will struggle with modern HD content on youtube, so forget about working on 4k footage in any kind of constructive manner.
Upgrading the RAM and storage won't help. It will make it more usable for browsing facebook and checking emails, but beyond that any mid range cell phone is a better platform for editing video.
If you really want to edit 4k footage, even the low bitrate files you get from the Mavic, you have little choice but to buy a new computer.
If your tied to OS-X when a mid range Mac Mini isn't a bad place to start.
Look at the 6 core i5 or i7 model with 16, or ideally 32GB of ram.
The base quad core model doesn't do hyper threading, so while its significantly faster than your old one, it's not really enough of a performance leap for smooth and easy 4K video editing, and is designed primarily for light tasks like web browsing and word processing.