There are many options available to the homebrewer for grain storage. This post will seek to describe the most common methods, their advantages, and their drawbacks.
The considerations for storing base malt and specialty grains are a bit different. Base malt is higher turn over and higher volume in comparison to specialty grains. A homebrewer may end up storing a couple pounds of a specialty grain for several years in some cases.
The simplest way to store base malt is to keep it in the bags it came in. When a bag is partially used, a ziptie can be used to reseal it. This works well for many people who do not have any pest concerns, or store their grain indoors. Additional levels of protection or organization can be combined with this method, such as keeping the bags of malt on a shelf or off the ground somehow. Some will store these bags of malt in totes, or in the most extreme cases, in sealable barrels.
Alternatively, base malt may be moved to a different container – such as a large sealable plastic container or 5 gallon buckets. Large plastic containers or totes have the advantage of coming in clear plastics allowing you to visually monitor your inventory, being cost effective, and coming in a variety of sizes. The seal they provide is not as strong as some alternatives, but likely sufficient if your storage area is dry and pest free. 5 gallon buckets are a somewhat more costly option, but do provide a good seal and a high level of protection to your grain. They are either utilized with gamma seals or basic snap-sealing lids. Two buckets are typically able to hold an entire 25kg sack of malt. A popular choice is also utilizing containers designed for keeping pet food or animal feed fresh. This includes Vittles vaults, which come in sizes large enough to hold an entire sack of grain, have stackable versions, but are expensive (made by same company as gamma seals). Or, slightly more affordable, air tight pet food containers. Which option you choose will depend on your budget, where you store your grain (moisture, temperature, pests), and your inventory turnover rate.
Specialty grains are suitably stored in any food safe container that is available in 1 or 2 gallon sizes (a 1 gallon container will hold 5-6lbs of grain). If you have many different specialty grains, a cheap option is a high priority. Bulk food containers can be reused for this purpose such as health supplement containers (known as wide mouth bottles, see here for an example) or spice containers (sometimes referred to as plastic oblongs, see here for an example). Large (1 gallon capacity) or extra large (2 gallon capacity) freezer bags work well also. Large glass or plastic jars, plastic buckets, etc, are all suitable storage containers. These smaller capacity containers are usually easier to ensure sealed. Personally, I use extra large freezer bags, which are stored inside the same clear plastic totes as my base malt as shown in the images below.