We live in a relatively small house for a family of 5 so we need plenty of storage but also storage that looks cute and holds a lot of things so here are some of my storage solutions!
What would be hard to use space under the stairs is home to our Ikea Kallax units which house toys and some electronic bits and bobs like chargers and cameras etc. We love these units so much!! We actually have four of the tall ones and three of the smaller ones throughout our house! We have one of the taller ones in out upstairs hallway which is half a bookshelf for all of the kids books and half storage for us for files etc. I would definitely recommend shelving or units that you can store things in as they may take up floor space but the tall unit can hold 8 canvas drawers of things which surprisingly is quite a lot!!
I also have a love of baskets, I found some relatively cheaply in Tesco and they are quite pretty too and I put them above my kitchen cupboards with bits that I don't use very often inside which frees up cupboard space for every day things! You could also look to do this above wardrobes etc as well.
Personally I have the under bed storage boxes on top of the wardrobes to store things in and also under the bed! There are other under bed storage solutions such as vacuum pack bags etc so lots to choose from.
I do also think that a big storage solution is to go through your things regularly and donate anything that you don't actually need or use. This is something that I tend to do every few months when things are starting to get a little cluttered and busy just to free up space and give us more storage again!
Short and sweet but hopefully one of these solutions will help you out :-)