I guess it depends on how much you have! A lot of people use a clip-it-up (either bought or homemade). I have way too many embellies for that. WAY too many, because I overshop like mad. I try to keep flowers stored in a few of those clear Iris containers. Then I have alphas in plastic storage bins that I got at the dollar store, separated by colors. Flat embellies are sorted by theme in two paper sticker binders (PSB). I honestly have so much stuff that I forget what I have. Unfortunately, I can't leave it all out due to space issues and very curious cats. I'm really eyeing up the clip it up floor model, but I'm worried my girls would chew the packaging. They LOVE plastic.
I used to store stickrs in a binder but it became too cumbersome, so now I store all my flat embellies (and some non-flat) on my clip it up (I have the regular one with a top tier added). I keep all my stickers, rub ons, and anything else that comes in a flat package (except letter stickers- they would fill my CIU!) on there and I love it!
I have to chime in on the Clip It Up. For Christmas I got one with the top tier addition, and I love it to pieces. I cannot believe how much it holds. I had three Iris boxes stuffed to the gills: one for rubons, one for stickers, and one for other stuff like diecuts, flowers, borders, journal spots, etc. Everything fit on the Clip It Up - once I got the extra clips. It's so nice to be able to see what I have without going through all the different storage containers.
eta: All my alpha stickers are still in an Iris box.
Just wanted to throw in a bit of caution if you are new: It is EASY to overbuy. Ok, well, even if you are not new, it is easy to over buy.
In particular, newbies tend to stock up on stickers. This may turn out to be a mistake for you. I don't know your scrapping style, but many scrappers find that they rarely use stickers as they get a little more advanced.
What is cute to you now, may not appeal to you by the time you get around to a project with that theme.
Anyway, if you don't buy a lot then you don't have to store them. For stickers, let the stores store them! And just buy specific stickers as you need for a particular project. If you already have a large sticker collection, then a clip it up is probably the most useful and user-friendly system.
i have gone through a lot of different ways to store my stickers. i had bags, drawers, sleeves. the one thing that has worked the longest is the Cropper Hopper Expandable Paper Organizer. its long enough to hold them and i can still see everything.