Learn Hardcore Spanish (Latin America): Estoy cansado, así que voy a descansar un poco.

Because estar generally refers to a temporary state or condition (being tired in this case), while ser refers to a more permanent or inherent characteristic. Saying Estoy cansado indicates that you feel tired right now but won’t necessarily remain that way permanently.

Why is it cansado and not cansada?

In Spanish, adjectives must match the gender of the speaker or the subject. If a man or a boy is speaking, he uses cansado; if a woman or a girl is speaking, she uses cansada.

What does así que mean, and can I use other words instead?

Así que means so in this context, linking the reason (being tired) to the result (taking a rest). You could also use similar connectors like por lo tanto or entonces, but así que is very common and natural in everyday speech.

Why do we say voy a descansar rather than the simple future descansaré?

Using voy a descansar (the periphrastic future) is a very common way in Spanish to express immediate or near-future actions. Descansaré is just as correct but tends to sound slightly more formal or less immediate. In everyday conversation, voy a + infinitive is extremely frequent.

What does un poco refer to here, and can I say something like un rato instead?

Un poco literally means a little (a small amount), referring to time spent resting. If you want, you can say un rato (a while) instead, which also sounds natural. Both phrases convey a short amount of rest time, though un rato might imply a bit more time than un poco.