Card storage - probably the thing I think about the most in the hobby that makes me slightly not enjoy it. It really depends on how big your collection is, and also what you are planning to do with your cards. If you are collecting with an intent to sell the cards and make money, then it is probably better to have them in sleeves and toploaders in a box. If you collect cards to actually collect instead of invest, then you can pretty much store the cards however you prefer.
Pages and binders makes for easy viewing, but that can take up a lot of space and cost a lot of money. There are differing opinions about how safe cards are in pages, but many say that if you use high quality pages like Ultra Pro Platinum and D ring binders then you should be okay. Personally I would love to have cards in binders to look through, but I don't have the time or the money to move everything to binders right now. Maybe one day I will have some of my favorite cards in binders.
Penny Sleeves and toploaders can be a good compromise of protecting your cards and still being accessible enough to look through.
I don't collect to invest and I have never sold a card, so the protection part for me is more so protecting the card I have for myself rather than worrying about future value. I actually don't use anything other than BCW carboard boxes to store my cards. I don't use sleeves or toploaders or pages. I have my collection held in multiple 3200 count boxes. This works for me since it takes the least amount of space and costs the least amount of money.
I will say though that looking through my cards can be difficult, and I need to figure out a way to make it easier to enjoy my collection. I am thinking about creating some sort of hierarchy for my cards to move them into smaller collections. But I have been thinking about this for years, and I find I just don't have the time to do a big project like that. And also I think about what I will do when I get new cards. It is already hard enough to move cards around to put older cards where they need to go, and that would be much more difficult if I have multiple smaller boxes or if the cards are in pages.
I think maybe I have come up with a 3 tiered system I might eventually do. I am thinking about moving all my cards of my favorite teams, all star players, and hall of famers into smaller single row boxes. And then eventually moving my favorite teams, hall of famers, rookie cards of all stars/hall of famers, and inserts of all stars/hall of famers to pages and binders. So then I will have non stars in the 3200 count boxes, stars in the single row boxes, and my showcase cards in pages. But I collect NBA and MLB cards. I think this is great for NBA, but there are so many more all stars in MLB that I still am not sure about the whole thing. And on top of that the baseball hall of fame has not elected Pete Rose, Barry Bonds, Roger Clemens, Mark McGwire, Sammy Sosa, Alex Rodriguez etc, for various reasons so it always feels silly thinking nope A Rod and Bonds don't go with the rest of the legends. I grew up watching baseball in the 90s and early 2000s so my childhood memories are filled with watching the steroid era guys. So not adding them doesn't feel right, but then that means my system is broken. Not to mention when it comes to all stars, some guys have never made an all star appearance but have had much better careers than other players who can be considered all stars because they either had one good year, or were a questionable selection to begin with.
I am writing a novel, but to summarize it really comes down to what works for you. Toploaders and sleeves will probably give you better protection than binders and pages, but you will probably enjoy your cards more leaving them in the pages.
Hopefully some of this helped, but the reality is that I myself am never really sure what to do with my own storage. And in the end for me it all comes down to time and money and my cards will probably remain in the 3200 count boxes for a long time. And also I can never come up with a system I am satisfied with enough to actually make the change.