There's a lot to consider when choosing a mini-ITX case. Space will be scarce, as you won't have room for multiple graphics cards or a stack of SSDs. Proper cable management is going to be your friend through the entire process, and you'll need to be careful when it comes to component selection too. If this is your first build, a mid-tower case will give you more room to work with—but that's cheating.
If you want to build a budget gaming PC, you're better off with a full-size ATX motherboard, as they are much cheaper, but a compact Mini-ITX case with an included PSU can save you a few pennies. Think about the lifespan of your components, though, as you'll have much less room to expand in the future. If you've got some cash to spend, though, consider liquid cooling to address any thermals issues that come with working with a smaller case.
We want to note that your choice of graphics card is far more critical with a Mini-ITX build. It's not just about length either, as cooling is a far greater concern when dealing with cramped interiors. Generally speaking, mini-ITX is one of the few times where using a GPU with a blower cooler is often the best decision. Unless you get a bigger mATX case with more airflow, you want your GPU to vent all that heat outside the case.
A little research should eliminate most potential problems and ensure your machine can handle demanding games and storage expansion for the next few years.