PhD student working on geomagnetic storms- these storms would cause changes in the earth's magnetic fields of hundreds of nanoTeslas, and cause electric fields of a few (<10) volts per km. Only reason why power networks are affected is because they span hundreds of Kms.
The geomagnetic storms are generally over long periods- low frequencies. From a quick glance at Wikipedia, this is unlike an EMP.
Solar storms can be extremely damaging to the power grid (and by extension, to electronics that is plugged directly into that grid). But, as you note, the distances required to produce a strong current are just too great for any home electronics to be affected.
There's a lot of mythology surrounding this, largely because valid information on nuclear EMP is conflated with EM effects accompanying CME (coronal mass ejections). There is some overlap between the two, but the differences are far bigger.
If your HDDs (or any other equipment) are inside a metal enclosure (like a standard PC case) and you unplug all external cables from it, it will be just fine. Any kind of metal enclosure with holes smaller than the wavelength of the radiation acts like a Faraday's cage, external EM field will not be able penetrate it. Solar storm generates a low frequency (very long wavelength) electromagnetic waves, so even a steel reinforced concrete construction (or any other metal net) with a good grounding would completely stop it.
Standard advice: the best thing you can do for protecting data is have an offsite backup. This could be as simple as Dropbox, Google Drive, Amazon S3, etc.
1. Cloud storage is likely to have a more resilient backup strategy;
2. Magnetic storms tend to be localized so you want to spread geographically. So if for example you copy data to hard drives and store them at home and work you're still in danger to a localized storm; and
3. And this is the big one. A single physical location exposes you to far more likely risks than solar storms such as fire, flooding and theft.
The geomagnetic storms are generally over long periods- low frequencies. From a quick glance at Wikipedia, this is unlike an EMP.
I really doubt they'd affect equipment like HDDs.