Whether it is a dozen of dimes of a pot teeming with cents, you should store them in coin tubes made out of inert plastic. If you have a handful of coins, you can store them in a glass prescription bottle but if it shatters by mistake, you will spend hours at a stretch picking up the splinters of glass. Hard plastic coin holders are the best bet. Your budget has to include storage media for your coins. You should never use soft plastic bags such as those, which are used for food storage.
You can also choose the plastic 2x coin flips. Do not use those made out of PVC plastic. Mylar flips are a much better choice but it is inevitable to careful at all times because removing and re-inserting coins can cause damage. Thus, you should be very cautious especially with silver and gold coins. Paper and plastic flips are not good for long-term storage. You should not store coins in them for more than six months. The fact that they are not airtight can cause potential damage to your coins if you store them for long.
The same is the case with cardboard 2x2 holders. These come with a Mylar window, which enables you to see both sides of each coin. However, these need to be stapled shut. Be very careful not to staple them too close to the coin. You have to staple on three sides for coin safety. Also, you could flatten the legs of the staple with pliers so that they remain in place and don't damage neighboring coins. Remember that staples will rust but there are always stainless steel staples, which you could choose.
Coin boards and coin folders can also be used for storage. These come with holes for mint and date. Most likely, you will storage with these. These will enable you to see only one side of the coin because they have a paper back. The downside is that they expose the visible side of the coin to fingerprints, pollution, and contamination. Thus, these are ideal for circulated coins. For uncirculated coins, you have to be overprotective. Don't even bother removing the proof coins, especially the gold ones, from their packaging.
Album pages are ideal for circulated coins. They have plastic strips and will let you see both sides of your coins. You can choose better albums, which come with inert plastic holders to hold the coins. These are similar to those which the grading companies use and can thus be used for uncirculated and proof coins.
Many collectors use coin folders because they come with numerous collecting aides. For example, they have a hole for the date and under the hole you can see the mintage figure and this will let you know how rare the coin is. You will also see coin facts such as composition, diameter, weight, etc. on the flyleaf.
Canvas mint bags are not ideal for coin storage at all. This is because they are not resistant to contamination or water. Also, when you move the bag, the coins jiggle and scratch against each other. Don't even think of storing coins like this, especially if they are valuable.
The Mint may use plastic tubes and plastic wrappers to ship coins but they are not ideal for storage. They barely provide any protection. They can easily tear and contamination and water can seep through easily. Soft plastic tubes have open ends and provide very little protection. Paper wrappers are not the right choice for upper grade coins.
Some of you may have chosen aluminum foil to store some coins. Get them out immediately. Such storage will cause coin corrosion because of metal-to-metal contact. This I found out after unearthing Morgan dollars from the damp floor of a garage, wrapped in aluminum foil. All coins had suffered enough damage to break my heart. Shoeboxes can contaminate your coins. Use a plastic bin instead, with a nice tight fitting lid so that you keep the air out.
The bottom-line is that you should take very good care of your coins. Bowls and cups are NOT the right place for your coins. It will hurt you exceptionally if any coin loses its value because of dings and scratches inflicted on them by your carelessness.
Keep cardboard, envelopes, tissue paper, and other papers except 2x2 coin flips at bay because these contain sulfur. Sulfur has the potential to blacken your coins. Cotton lined flips are good but you shouldn't use them for a long time. Always use products, which have been designed to protect coins.
Know that even if you care exceptionally well, some damage is bound to happen to uncirculated and proof coins. They may tarnish or discolor. More often than not this is because of the exposure before packaging. You may suddenly find a change in color or fingerprint on your safely stored prize coin. Don't be surprised because this may be because it was exposed before it came into your possession.
"Loose lips can sink ships" was a popular saying back during the World War II. The same must be your slogan because if you brag about your coin collection, you may end up attracting burglars. Tell your friends and relatives very clearly that bragging about your collection will only increase the risk of the coins being stolen.
Coin dealers are extremely careful and try avoiding this problem as much as they can. It is not rare for thieves to follow dealers for many miles after leaving a coin show. They break in the vehicle the first chance they get. If you want to stay safe, don't go parading with your coins.
It is also wise to rent a post office box so that all your mail goes there and is not addressed directly to you. Remove your address labels from all papers and envelopes before you throw them away. Invest in a paper shredder if you can.