Having a huge ass internal drive (or a few for that matter) is the cheapest and most convenient way to go.
You can pack 8 2TB drives in most cases for a total of 16TB of storage for a few hundred bucks. If safety is your concern you can connect them in RAID1 so you will have all your data backed up on at least two drives.
Seriously, an internal 2TB drive costs like 50$ these days? You will have all of your data on your computer with fastest and easiest access to them, not limited by the speed of your internet connection which even with a 100mbit connection is numerous times slower than probably all modern hard drives. Also even the easiest cloud storage - Dropbox stores your files on their servers and your computer at the same time so you don't gain any hdd space anyway + the dropbox app uses your resources.
The only reason why cloud storage makes sense is when you access your data from a lot of different devices but honestly, I access my data from my computer, laptop, mobile phone and university computers and still don't find cloud storage convenient enough. I have a Dropbox account because that's always 16gb (that's what Dropbox offers after you verify your edu email address) of free storage but I use it only to upload files from my phone when I'm low on memory for example when I take a lot of pictures or videos on vacations.