Looking to go live what do i need to know

I'm going to bump this thread because I have the same question. I'll provide some information as to what I'll be doing as well.

I'm looking to do some live streaming and I need some help. I need to find a good streaming card and some tips as to what kind of speeds I need for the internet.

What I have: Asus Gryphon Z87, i5 4570k, 32GB of G. Skill Ripjaws ram, Nvidia 660, 2 SSDs and a 10k RPM drive.

What I want to do: I want to do a live four camera stream with one input. one on the audience, one on the commentators, one on the stage and the last on the participants. I also what to have an input from an XBox as the final input.

To reiterate: What kind of capture card do you recommend? And how fast should the internet be?

BUT WHAT THERE'S MORE: What kind of software do you all recommend for streaming? And what kind of control surface do you recommend for that software.

Bonus!!!!! Are there any streaming softwares that allow for python integration? I have a control surface that can do the job but I need to program the settings in python so I can use it.

Edits:
I'd prefer to do this with HDMI.
I'm probably going to stream via Twitch.