The larger sized Ziploc bags are in the storage section of your big box stores - same place you find plastic tote bins (usually). I buy 3 gallon, 5, gallon, and 20 gallon bags for everything from brining to storring dry rubbed meat overnight.
3 gallon bag is perfect for 1 BIG pork butt, two whole chickens, or two family packs of chicken parts.
5 gallon will fit a small turkey, two butts with brine, 3 or 4 chickens with brine, half racks of ribs.
20 gallon can fit up to 2 15-20 lb. turkeys with brine! Also good bags for long items like belly's or full racks of spare ribs.
A great way to use these for brining is to put your brine and the poultry into whatever size bag you need, then place into an ice chest that is roughly twice the size of your bag, and then fill the ice chest with ice. The brine does not get diluted from the melting ice, and you can set it in your garage overnight and still have it stay plenty cold for safety - I usually have at least half the ice left unmelted after 24 hrs. or so.