Actually, I stand by my list, last updated in the thread linked in my signature. Not a lot has changed for home backup - AGM batteries are still the best bet. There are two recent developments - The lastest ResMed pump seem to use more power than before so they will need a bigger battery for the same coverage, and Lithium packs have come down in price, so that some people may want an "overnight travel" pack that can also serve as one night back. But for more than minimal needs, the AGM batteries I outline are still the best bet.
That said, I have, to some extent, avoided very specific "parts lists" for two reasons. First, my approach is very generic, and at any given time there may be better deals with, for instance, the various brands of AGM batteries - the particular battery I used almost doubled in price a few months after my first post. I do like the BatteryTender line of chargers, but there are several equally good brands that may satisfy your needs better. In your case, the battery for a 10 day outage may be too large to be quickly recharged by the small BatteryTenders.
The other reason is that I want people to understand the basics of the system so that they can make informed decisions to satisfy their needs. Details such as the size of the battery, the particular battery charger, whether to use a splitter to charge cell phones, what kind of case to use will be different for each user. I've often mentioned the U1 battery as being in the "sweet spot" but some users will want a smaller, lighter battery, others will want a 60 pound monster. Personally, I have a bank of 4 60 lb batteries, but I'm running a refrigerator! Every need is different, and my goal is to give the best, basic info.