Personally I would recommend a Generac Rapid start 5500, which retails for about $ 659, but you can likely buy from a local Generac dealer for less. Try to track down a Generac dealer/electrician in your area, as they can get you a better price on the unit and install anything you want to add on. I purchased a 5500 last year, and had an electrician hook it up with Generac's new transfer switch. The 5500 is powerful enough to run my 300 gallon reef, and a variety of things within my home. While this may be over-kill for what you want, the Generac transfer switch makes switching from utility to generator power as easy as possible, and can also run some stuff in your house if you want. Also, the transfer switch is totally upgradeable if you decide in the future to get an automatic generator. I don't know of any Generac (and they are a world leader) generator that can kick on automatically, other than there whole home automated generators. However, with the transfer switch, other than starting the generator - that's all the work that a 5500 requires. You can purchase smart battery back-ups for computers that connect wirelessly to the internet, and will notify you in the event power goes out. I have my router and modem connected to one, so that if power goes out, I still have internet access enough for the back-up to notify me, so that I can make arrangements to get my generator up and running. While this is likely more than you wanted to spend - it beats spending 3k+ on a whole home automatic unit, and offers much of the same reliability and ease of use.
As for having a Generac non-automated whole home unit kick on, we install and maintain Generac generators and I am not aware of that feature being possible on anything other than whole home automated units. In fact, any of the standard generators require a pull start, or switch to start. The rapid start system is much easier than traditional generators, and either requires one or two good pulls to start, or turning a switch if it has electric start. Even the new transfer switch doesn't have the ability to start the generator automatically in an outage.