I'm reading Yotsuba (1st chapter) and I have come across the sentence
The sentence translates as "WELL I'LL GO GET SOME STUFF THEN. YOU STAY HERE AND CLEAN UP." I'm having trouble understanding what the きてやる means in じゃあ俺が用意してきてやる. I've found from this link, https://www.kanshudo.com/grammar/%E3%81%A6%E3%82%84%E3%82%8B , that てやる means that someone is doing something for someone else. That makes sense in this situation. Unfortunately, I do not know what purpose the きて is doing here though.If the sentence were じゃあ俺が用意してやる then that would make sense. The きて makes me think that this is perhaps some "auxiliary verb." Something that I am not very good at recognizing. If anyone could help out, then I would really appreciate it.
Also, if it's not too much trouble, I would greatly appreciate someone telling me where the て comes from in 片付けてろ too since jisho says the verb is 片付ける.
Big thanks to whomever can help. I'm finding that reading is hard.