Over the years (decades) I've gathered up a lot of coins - valuable and not so valuable, hammered, milled and undecided and in every metal that is commonly encountered. I've tried different storage methods, some I like and some I don't.
Some thoughts
PVC coin envelopes
These are generally considered to be a no-no when storing coins - especially silver. Personally I don't keep anything much in them long term - but I have had "junk box" type coins in some for 30 years or more and they haven't changed a bit.
Non plasticised clear envelopes
These are more brittle than the ordinary PVC ones (Saflip seems to be one of the more well known brands) I have very few of these and don't really like them. They are supposed to be less harmful to coins but they can only really be stored in coin boxes and you can't write anything on them.
Flips
I'm sure these have other names but a lot of people know them as flips. I don't really like these and don't use them at all. Mostly closed by stapling (can be an issue in itself) again a coin box is probably best for overall storage but you run the risk of a bad staple rubbing against something it shouldn't. There's also not a lot of cardboard for writing on so a large coin can be fiddly.
Coin Albums
There seems to be two types of these. Ones where you insert the coin directly into the plastic page and ones where you insert an entire holder into a plastic page. Again I don't use these at all. I did as a child and had loads of issues, coins falling out, some discoloration, pages ripping because of the weight. Of course, products are probably much better these days and these issues may not arise but I could never go back to them.
I have only ever seen pictures of those Dansco type albums so can't comment on them.
Capsules 
I have a few of these but not very many. The only coins I have in them are some modern proof silver (about 40 or so). Those proofs are the only coins I have where condition really matters. Overall storage is a bit more tricky - so at present they just lie in the bottom of the cabinet.
Acid Free envelopes
The vast vast vast majority of my coins are stored in these. Pro's are that you can get the coin out easily, they store well in coin boxes and you can write a small essay on the envelope. The drawback is that you have to get the coin out of the envelope each time. I guess it really depends if that is a drawback or not - for super high end coins it probably is.
All the envelopes are in boxes like the one below:

and all the boxes are in old cassette storage suitcases which I find are perfect.
Trays
Both Lindner and Lighthouse do these and I have about a dozen or so. I keep Roman, Greek and some silver in these and I find them perfect for the job. Stack-able - they don't take up that much room and it's easy to get at the coin in question when you want. They are made of inert material so long term storage shouldn't be an issue
The Cabinet
This is where my best coins go. Thalers, crowns, rupees, etc. My version holds over 1,100 coins so it's quite big and should last me a lifetime. Pro's are that it looks great and the coins just look fabulous on the trays. Mine's an old one made of an inert wood so I'm not worried about fumes etc. I should add that all my coins were circulated to some extent so any minuscule rubbing on the velvet won't matter nor will any small toning.
I realise that everyone has different needs but I find that acid free / Tray / cabinet combination works for me.