When our local disaster relief organization educated us about how tenuous our nations food chain is, I decided to amend my existing tightwad tendency to buy in bulk when on sale into an organized food storage plan. The Latter Day Saints food storage calculator website is a good starting point to compute how much food your family might need, though you'll probably need to amend it to suit your families eating habits as I personally doubt our family would ever get into grinding our own wheat. Over the past 3 years I've gradually built our 2-week stash into a well-rounded 18-week supply, with probably another 6-8 weeks of not-so-well rounded eating.
Once you start storing more than 3 months worth of food and supplies, you do need to start paying careful attention to the shelf-life of foods and be sure to actually cook and eat the things you are storing (like dried beans, which everybody acknowledges are cheap and healthy, but we all "forget" to put out to soak the night before). Canned goods -could- be eaten past two years, but they start to lose color and flavor so you have to be sure to keep them well marked and rotated. Dried grains and legumes can succumb to mealy-type bugs. We have these annoying little brown moths in our area which get into everything and leave their filthy little larvae munching through our dry goods!!! Putting bay leaves in the flour and pasta bins didn't work, so right now I'm experimenting with keeping little muslin bags of cedar chips on the shelf next to them (will let everybody know how that works). Specially prepared freeze-dried and vacuum packed "survival foods" last much longer without deterioration, but they're also very expensive so I've been reluctant to stock up on anything but the hardest-to-keep items (like powdered eggs). My goal is to build our supply stash to 1 year, but I'm also committed to not breaking the bank or losing perfectly good food to waste while doing it.
I would suggest that Brandy start by creating a price book a'la Amy Daczyzyn "Tightwad Gazette" and use that $5 per week she has budgeted to buy extra of whatever is on sale. She should also read up on root cellaring, canning, and general food preservation (even if she has no plans to build a root cellar or can vegetables) so she has an idea about what foods store better under which conditions. She should also invest in a good open storage system that will work in her home (such as shelves or under-bed storage bins). If space is tight, she could look for unused "dead areas" in her home, such as the 4-5" space behind doors, along hallway walls, and above her head, to put shelves (2x4 shelves are cheap and just the right width for canned goods). Once she's started to build up a 6 weeks reserve of sale items she uses the most, she can use the LDS website and other "emergency preparedness" lists to help her refine her food storage plan to fill in any gaps she might have. With only $5 per week budgeted, this will take time, but if she persists eventually she'll build up a pretty nice stash -and- save a bundle of cash.