Protip #1: Buy someone elses collection. You can get cards on a massive discount because they just want to unload their collection quickly. I'm often talking 50%+ discount (you'll save at least $100.) Then you can buy the rest of the cards you want from wherever.

Protip #2: Don't go with binders. I did that for a while, and not only does your collection eventually outgrow pretty much any binder storage solution you have, it also becomes a nightmare trying to organize it. How do you sort the cards? Unless you do it by release date, you'll have to insert cards between other cards, and you can't predict where. So you end up shifting cards around every time you get new cards. This isn't a trading card game so you're not going to be doing much binder trading.

I would recommend either (a) a cardboard card box like the BCW trading card boxes or (b) this transparent plastic box. 3 of either of them should easily hold every card you'll ever need and are portable. I added these card dividers that stick out to keep them sorted by faction, then by type, then alphabetically. The dividers come in lots of colors. I got 6 different colors, and use 9 of each (1 per faction, plus 1 for neutral corp and 1 for neutral runner, and they come with 10) to make it easy to find each part of my collection. The dividers work for either solution. Alternatively, you can easily make your own dividers in a variety of ways, e.g. cutting index cards (possibly of different colors) to size, for super cheap.

https://www.amazon.com/KMC-Card-Box-1000/dp/B0007N7P8K

This is double the price it is in Japan, but might be reasonable. I have two of these for Magic, and they are good for both sleeved and unsleeved cards, and have inner compartments that may or may not fit your needs.