If you are in a good wind area and have a wind generator, you can probably cut this down a day. To figure how many amp-hours storage you need, take your average daily usage in watts and divide by the battery voltage. If you want to keep running for 4 days of bad weather with no sun, multiply that times 4, which gives you about 850 AH total capacity. UPS and backup power systems are the same, except that the times are often in hours instead of days. This is what most people look at.
Batteries are the component that are most often skimped on, but can make or break a system.
Price is a fairly good indicator of the overall expected life when used in a particular application, with the exception of the Concorde AGM's, which are a special purpose sealed battery. There are exceptions, such as occasionally stumbling over a pile of 4-year old telephone batteries, but they are few and far between. In fact, we usually do not recommend ANY used batteries - regardless of the price. This is what really determines the long term cost, but sometimes the up-front costs can be higher than what was expected. There is more to the lifetime cost of a battery system than just the battery costs up front - you have the interconnects, shipping costs, maybe Hydrocaps or Water Miser caps, maintenance, and eventually disposal.