"You clearly did not read the article I linked to. All the reasons you list above why peak-oil might not be an issue have been taken apart in that article (and each one in more depth in many other places) already, so I'm not going to repeat it here."
I read much of the article, but it was very long and rambling and essentially just poorly referenced alarmist tabloid journalism. Many sources it did link to were just mainstream media and I see no reason to take it any more seriously than I would the rest of the media. Nothing was really "taken apart" as such. Rather dismissed as it didn't fall in line with the agenda of the author (neither an economist nor an engineer, so why does his opinion count more than mine?). There's much better stuff on [link]
Anyway, no single alternative will take over from oil, but if you look for them there are plenty of contenders that are not taking off as they are not cost-effective with fossil fuels. As the prices for oil and gas rise over the next few years, some of the alternatives will begin to be more widely adopted. Look up some emerging technologies, some of them are fascinating. I particularly like the trochilic rotary stirling engine, low-input biofuel crops such as the use of jatropha in India, recent advances in automated plastics separation for recycling etc, and I'm watching developments in LED lighting closely as I don't like CFLs much at all...
"As the richest and most powerful people and some of the biggest companies in the world prepare for peak-oil, I don't see why I should ignore the problem. So me and my family are preparing for it, and that includes having very-low-power ARM-based computers available."
I sincerely hope you're doing something more proactive than that, or it's just rearranging deck chairs on the Titanic. I have cut my gas consumption by 75% in the last 4 years. The electricity my PC uses is way, way down the list of priorities.
"Finally, if peak-oil should really turn out to be a non-issue, we will still be better off, as most of the things we do to prepare for it, make good financial sense anyway."
It won't be a non-issue. But if we suffer serious consequences, your electricity bill will be the least of your worries. Food shortages will hit first.