Suggestion on streaming PC

[Kiaeneto]

Recently just built my gaming pc and got an audio setup for streaming on twitch. I haven't started streaming yet and was looking into getting a second pc for the streaming part. What are the bare minimum pc specs do I need for a streaming pc so I can stream my gaming pc to twitch?

My gaming PC and audio setup.

 

[King Dranzer]

What is your budget?

 

[Kiaeneto]

I would say around $1000 and would like to have it as small as possible case wise.