Uninterruptible Power Supply, a battery operated backup power mechanism made for computers. I have an older model one that's similar to this and it's really nice not to have the computer kick out every time the power blips for a few moments to ten or fifteen minutes. We get a lot of thunderstorms in the Summer and the power often goes out briefly after lightning strikes.
http://www.amazon.com/APC-BR1500G-BACK-UPS-10-Outlet-1500VA/dp/B003Y24DEU/ref=sr_1_6?s=pc&ie=UTF8&qid=1374360712&sr=1-6&keywords=ups+battery+backup
Inverter generators like you have posted a link to are particularly good on fuel efficiency at partial load but they are also more expensive to buy and more complicated than a non inverter type generator, I'm skeptical that you need that feature for your purposes.
As for the reliability of a Honda generator, I think it will do well. We have two Honda motors of that type here that have run a combined total of thousands of hours over more than ten years with almost no servicing at all.
For a whole house AC system you're going to need a lot bigger system and that would depend on the power draw of your AC, you could get by with a three or four thousand watt generator if you just wanted to run a small to medium window AC.
Something like this would probably run your whole house AC system too but you'd need to get someone knowledgeable to wire up a cord that will let you plug it into the generator.
http://www.amazon.com/DuroMax-XP10000E-Portable-Generator-Electric/dp/B0018C6BDE/ref=sr_1_20?s=hi&ie=UTF8&qid=1374361463&sr=1-20&keywords=yamaha+generator