Un XBox vs Una XBox
 

En mi casa hay una Playstation y una XBox.

¿La he escrito correctamente? (consola)
Es que me suena 'un' XBox...

Gracias de antemano.

Yes, because it's la station and la box. But your instinct tells you all new nouns in Spanish are masculine, what is also correct.

This whole thing is why in some countries it is la internet and la web, while in others it's customary to call it el internet and el web.

Es la porque se refiere a una consola.

As Alec pointed out, you'll hear it said either way depending on regional usage.
An online search shows that both articles are currently being used- 'una Playstation' and 'un XBox' being the more popular choices.