Xbox & PC Twitch Stream Setup

I’m ready to start broadcasting on Twitch from both my Xbox and my Windows-based PC, but I want the whole pipeline dialled in—from wiring the gear to polishing the on-screen look. Here’s my current position: I already own a good USB microphone, yet I’m still missing a capture card and webcam... (Budget: $30 - $250 NZD, Jobs: Audio Engineering, C# Programming, C++ Programming, Python, Software Architecture, Twitch, Video Editing, Video Production)