I reckon storage is largely down to personal preference, though price and long term flexibility might be a consideration.
Options range from a few pence (Colin Cooke sell acid-free envelopes suitable for coins, though obviously you can't view them without taking them out, at least there's plenty of space to write notes for your records!) to a personally made coin cabinet. I have one of Peter Nichols' The advantage is that you can select trays with coin recesses to the size you wish. In my case, all my coins are the same denomination, so the trays are the same. It has a traditional feel, helped by the fact that I use coin 'tickets'; small paper discs upon which you can write information about your coin. As several of my coins came with earlier collectors' tickets I think it's a nice way to store them all.
My 'secondary' collection is made up of coins of differing sizes and so I use a similar system to many others in that the coins are in 2x2s. Called 2x2s because they are around 2 inches square. Usually these are card with mylar windows:
though I have some plastic ones I bought years ago. Mine then sit in coin storage trays (Chris sells the Lindner version) though some people use albums (like photo albums but with little pockets in the pages as pictured above) to hold the 2x2s, which can be a bit cheaper.
Another option is to use coin trays but with round recesses to hold the coins directly or in plastic 'capsules' Again, Chris's supplies (click on the predecimal.com link top of the page) include these.
Main thing is to ensure you use new products that were designed for coin storage as these will be safe (no pvc or acids that can damage the coin).
Finally, there are coin 'flips' transparent plastic envelopes or double envelopes (one for the coin, one for a card to write details on). If you buy mylar ones these should be safe, but I'd suggest not using ones you might receive coins in when you buy them as it's difficult to know if they contain pvc. Paper envelopes from dealers and auction houses should in theory be acid free and hence safe!
As sound says, best to consider record keeping now as part of your storage and security. So it's worth keeping records of what you have, where you got it and how much it cost. Additional details like grade, likely value .. up to you. I use an excel spreadsheet, coin tickets, photographs and retain receipts/ copies of ebay/ dealer listings and keep electronic copies on memory sticks. Recreating records later after you've bought a few dozen coins will be tedious, a few hundred .. well, like I say, best start now! Also gives you a way to keep track of what you have (avoiding duplicates) and what's needed.
The collection might be worth but a few quid now but .. who knows what it might cost you to replace it I a few years time?
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