Some come with their own software for easy backups, however you'll also be able to drag and drop files around if you prefer to be in control. And whichever of the best external hard drives and SSDs you choose, you'll find that they're generally easy to use simply plug them into your Mac or PC via Thunderbolt or USB and you should be good to go.
If speed matters then you need to be looking at SSDs rather than hard drives while you'll inevitably pay more for a lot less storage, you'll get blazing-fast transfer speeds and, thanks to their complete lack of moving parts, much better reliability. Depending on how much you want to spend, you can get a small and inexpensive drive that'll easily hold your most important data, from simple documents through to larger video files, with room to spare, or you could instead invest in a full backup solution that'll hold everything on your main drive so that it's safe and sound if the worst happens.