I store my decks in This.
The 10 compartment one stores a bunch of commander decks great. Pretty much all the rest sits in a couple of shoeboxes.
https://www.amazon.com/Stanley-Removable-Compartment-Professional-Organizer/dp/B001G1CUK0
Works great, very modular, not too expensive
I use binders for commonly used cards and cardboard boxes for "bulk" cards (The cards you don't think you will use very often): 5000 capacity box, 800 capacity box
I also hear that these Stanley Organizers are also incredible for storage, as each compartment is the perfect size for a sleeved MTG commander deck (100 cards).
The binder should definitely be sorted. Not only is it more organized that way, you can find the cards you need much faster. The box can be unsorted, though I like to at least keep cards belonging to the same faction together.
This does run into the problem of occasionally not knowing whether a card is in the binder or box, but it has the advantage of giving you quicker access to the cards you most commonly use. I mostly do this because of habits from MTG, where you get tons of useless cards, but Netrunner doesn't give you nearly as many useless cards, so you could make the argument for storing all your cards together instead of differentiating between commonly used cards and bulk.
Your cards can be in whatever order you want: completely alphabetical, by faction and then by type and then alphabetical, by set, whatever. Your personal preference.
However, when it comes to sorting cards, or anything in general, there are fast ways to sort and slow ways to sort. Anyone who has studied computer science can attest to this. The difference is small when you only have a few cards, but quickly becomes massive as the number of cards grows.
Here are the two sorting algorithms you should know if you want to sort your cards quickly: Quicksort and Merge sort. They are among the fastest algorithms out there, they're easy to understand, and they're practical for sorting cards by hand. I'll explain them in the context of sorting cards below.
Quicksort
Here's how quicksort works for computers: Choose a "pivot" item at random from the unsorted pile. Now, go through everything and divide it into two piles: Those that would come before the pivot, and those that would come after the pivot. Then, sort each pile individually (usually with yet another quicksort). Once the piles are sorted, just combine them and put the pivot in between them, and voila, the pile as a whole is in order.
However, if you're a human, you'll find it more efficient to sort based on certain characteristics of the card that you can quickly identify (such as the card's faction) instead of whether or not the card comes before or after a randomly chosen pivot. In addition, you'll want to separate into multiple piles instead of just 2.
Here's an example: You want your cards sorted by faction and then in alphabetical order. You already sorted you cards by faction, and now, you want to sort your Anarch cards in alphabetical order. The cards you want to sort are in the following order: Wyldside, Demolition run, Deja Vu, Grimoire, Corroder, Medium, Yog.0, Stimhack, Parasite. The first step of quicksort is to divide the cards into piles. When sorting alphabetically, I like to make a pile for cards from A-E, one for F-M, one for N-R, and one last one for S-Z. However, as long as every card in one pile comes before every card in the next pile, it doesn't matter how you make your piles. So, dividing these unsorted cards into piles (according to my preferred sorting scheme), we get the following piles:
{Demolition run, Deja Vu, Corroder}, {Grimoire, Medium}, {Parasite}, {Wyldside, Stimhack, Yog.0}
Each individual pile is not in order, so we sort each pile individually (I would use another quicksort on these piles if they were bigger) to get:
{Corroder, Deja Vu, Demolition run}, {Grimoire, Medium}, {Parasite}, {Stimhack, Wyldside, Yog.0}
Then, we just combine the piles and we're good.
Merge sort
Here's how merge sort works for computers: Divide your big pile into 2 separate piles, and then sort those piles individually (Usually with another merge sort). Then, once the 2 piles are sorted, merge the piles into one sorted pile. The merging process is made much easier by the fact that the two piles are already sorted individually.
Here's how the merging process works: Look at the top item of both piles. Whichever one comes first gets added to the bottom of a new combined pile. Repeat until both piles are empty, and voila, your combined pile is sorted in order.
Example: You have the following sorted piles: {Demolition run, Yog.0, Wyldside}, {Corroder, Parasite}. The first elements of our 2 piles are Demolition run and Corroder. Corroder comes first, it becomes our new combined pile. Now, the top item of our 2 piles are Demolition Run and Parasite. Demolition run comes before Parasite, so it gets put at the bottom of our combined pile. The top cards of the piles are: Yog.0, Parasite. Parasite is put at the bottom of the combined pile. The second pile is now empty, so just put the rest of the first pile at the bottom of the combined pile. The combined pile looks like this: {Corroder, Demolition run, Parasite, Yog.0, Wyldside}. It's sorted, yay!
If you're a human, you'll be doing mostly the same thing as the computer. However, instead of having to lift up the combined pile to put a card at the bottom of it, you can instead make the entire combined pile face-down and add cards to the top. When you're done merging, just flip the combined pile upside-down.
Which one?
From experience, quicksort is a lot better if you have an unorganized mess to sort.
However, if you're adding some brand new cards to an already sorted collection, you'll want to use mergesort instead, since your collection is already sorted. Simply sort the new cards, and then merge the pile of new cards and your already sorted collection.
How NOT to sort your cards
Perhaps you currently sort your cards like this: Pull a card out of the unsorted pile, find out where it goes in your pile of sorted cards, then put it there. Repeat until unsorted pile is empty.
Or, maybe you do this: Go through the unsorted pile, find the item in the pile that goes below every other item in the unsorted pile, put that item at the bottom of the sorted pile. Repeat until unsorted pile is empty.
If they feel slow, that's because they are. They're mathematically inferior to quicksort and merge sort. The first method is actually OK if you want to just put back a card you took out of your collection, but if you have more than a few cards to add to your collection, merge sort instead.
THIS. Stanley Organizer. This thing holds multiple double sleeved decks and I ended up using one of the leftover spaces to hold tokens and dice.