How bad could we reasonably expect a solar flare to impact earth, and what can be done to mitigate the impact?

Space Weather is the field within heliophysics that tries to understand this Sun-Earth relationship. When a Solar Flare occurs multiple things may happen and how it interacts with the Earth and our technology depend on different factors.

The first effect, the X-ray radiation produced by an Solar Flare affects the ionosphere and therefore the radio communications. This effect is almost immediate and there's no way to attenuate or prevent it. We can forecast the likelihood of a flare to happen on the day but still we don't have the knowledge enough to exactly predict when it will happen. The radiation from the flare it takes around 8 minutes to get to Earth, and at the time we see it the radio communications have already been affected. This effects mostly to VLF bands.

After a solar flare high energetic particles and coronal mass ejection could be produced, these two events have different effects on Earth and whether interacts with Earth or not depends on where it happens on the Sun and the properties of the solar wind at that time. High energetic particles (also known as Solar Energetic Particle events - SEPs) could arrive around 30 minutes after the flare happened, and Coronal Mass Ejections (CMEs) between 2 or 3 days. These times depends on the properties of the events, not all are the same.

CMEs could be somehow predicted, and are these the ones that could affect, between others, the power grid. It won't affect your computer. The reason of why it affects the power grids is due to a induced electric current happened by the interaction of the CME's magnetic field produces in the Earth's magnetic field. The electric current finds it easier to travel through the power grid than through the Earth itself (the cables are better conductors). In simple words, when that happens the electric grid "thinks" that there is an increase of demand and tries to compensate it generating more electricity and that can burn them - as it happened in Canada in 1989.

To reduce it effects there are a lot of engineering work around these systems and I'm not an expert in such topic to be able to explain them properly. However, a warning to the power grids of a couple of days in advance helps. The difficult bit is how to be exact in the forecasting. CMEs sometime are deflected by the solar wind and just a flank of it "touches" the Earth, other times small ones get accelerated and have a larger impact than expected. So, to be able to reduce the effects we need to have a better understanding of their origin and surroundings, understand their physics and be able to model what they are doing. There are few models out there (e.g., CCMC) but at the moment we need to keep researching to improve these further.

Answering to "how bad" a solar storm (not just a flare) can affect Earth is hard to quantified, in UK it has been classified as one of the highest priority natural hazards in the National Risk Register, and similarly in other countries. An event like Carrington's (the one you linked) could have a lot of impact in our current technological civilization and it's been estimated in many years and trillions of US dollars to restore the damage (see Royal Academy of Engineer report on Space weather).