There are so many ways that you can show off your baseball cards, ranging from fairly cheap in price to very costly. It depends on your budget, the size of your collection, and how you want to display everything.
The most budget friendly (and also inefficient) wayto store your cards would be to put them in boxes. It works for the casual hobbyist and young collector alike. Most people who choose this route pick it because it is easy. It will protect your cards from damaging UV rays and some other pesky elements, but it isn’t really displaying them. So if you would like to brag about your collection or have it organized in some way, this is not a viable option for you.
Another low cost option that takes up minimal space is a binder (or binders) with pocket pages. The front and back of the card remain visible, the cards are still protected by the light (as long as you don’t get a transparent binder), and your collection can be organized any way you wish. When you run out of pocket pages, you can easily and cheaply get more. Run out of binder space and you can pick up another. I liked this method as a kid because it was easy to set up, easy to bring with me everywhere I went, and the cost fit well within the confines of my allowance. The drawbacks to this method are that it isn’t really foolproof—you can damage the cards just putting them in, bending the corners or accidentally creasing a card. Also, because the pocket pages are not completely sealed, they are not totally protected from liquids or other damage. Also, the portability factor can be a liability if, say, you forget your collection on a bus or at a convention. Yes, I am bringing that up because I’ve done it. Luckily it was before my collection was really worth anything and it wasn’t everything I had, but it still sucked. The cards also aren’t really on display like this. As your collection grows, you also need room to store the binders, whether it be in a bookcase, on shelves, or in a closet.
My other two ideas are more for the collector who wants their cards out on display. Single card displays are a choice if you have a breakfront, curio cabinet, or bookcase you can use to showcase your collection. These card displays are often made from hard plastic, are sealed, and are easily displayable. Especially if you have any cards that are autographed, be sure to get a case that offers UV protection. Put the display away from direct sunlight and heat to keep the cards looking great no matter what display you put them in. I have a lot of the shop cards in these under glass. It makes it easy to show a single card to a potential buyer, and the cards always look good displayed this way. It can be costly to put every card you own in one of these depending on the size of your collection, however.
An option for those of you with a lot of cards, if you have the money and the wall space, are wall-mounted display cases. Good cases are expensive, and the more cards you have the more you will shell out to give them a good home (and the more wall space you will need to mount them to). There are some monster sized ones that can hold 200 cards, and much smaller ones for a few of your favorites. They typically sell these as graded or non-graded, so pay attention to what you are ordering. I have one of these at home so that I can keep a small collection of my most treasured cards in sight.
Hopefully, this will inspire you to think outside of the box for your own collection of cards!