Backup power is kinda my shtick.
For the least hassle and automatic transfer a UPS would work well. The P35i has a running wattage (Power Factor not considered) of 180W. If we correct for mediocre Power Factor that makes it almost 250W.
http://www.apc.com/resource/include/techspec_index.cfm?base_sku=SUA1000XL This model plus one external battery from APC will run the insert for ~5 hours. The whole setup will cost around $1000, but the insert will never know the power has failed, fail-over occurs faster than you can blink. That UPS has a 1000VA capacity, so you can add a lamp and the entertainment center to the UPS as well, with a reduction of run time however. The ups also acts as Surge and Brownout protection. Increased run times can be easily obtained by adding additional external batteries.
Second option is a Genset. Permanently installed whole house units are nice, but overkill, and often cost more in maintenance than a portable model. The best bang for the buck in portables is the Yamaha EF series inverter generators. Honda has the market, no doubt, however Yamaha has a more serviceable unit, lower EMI and RFI figures, similar noise and fuel consumption at better price. The EF2000iS would happily putt along, very quietly, for 10 hours on a gallon of fuel running the insert and the entertainment.
I also like the UTS6 Automatic transfer switch from APC.
http://www.apc.com/products/resource/include/techspec_index.cfm?base_sku=UTS6
It allows you to select up to 6 circuits to have backup on. The nice thing about the UTS6 is that you can connect the UPS (above) to the panel as well as a genset, and have it all tucked away wherever your house panel is located. So if you aren't home, the UPS powers loads until you do get home, then you can connect a genset. All automatically. There is also a very nice priority mode, meaning(hypothetical situation): You connect the refrigerator, 2xLiving room, and 2xBedroom circuits to the UTS. The insert is on 1 living room circuit. The kids are playing with the vacuum (IDK why, they are kids) in Bedroom 1. The UTS notices you are reaching the 1000VA limit of the UPS and disconnects Bedroom 1 until the loads reach a level the UPS or Genset can sustain. Living Room 1 (pellet insert) is never disconnected. You get all that love for $400. Not too bad considering the prices for some really cheesy manual transfer switches.
Take care,
Ken