Even if it's just a shack, I want my own place.

Literal

Makeshift-hut [even-でも] good [because-から] own [attributive-の] house [subject-が] want.

掘っ建て小屋 ('shack, makeshift hut,' literally 'dug-post hut') refers to a crude dwelling built by driving posts directly into the ground without a proper foundation. Used as a stand-in for 'the most basic possible shelter.' ~でもいいから ('even X would be fine, so...') is a concessive pattern expressing lowered expectations or desperation.