you cant get a hat but this week you can click the beta at the top of the screen and click beta team.

If you mean a CRT TV screen, they are electrons. Beta particles are also electrons but of higher energy than in cathode rays. Modern flat panel TVs are purely electronic and involve nothing striking the screen.

So the precise answer to your question is neither.

No, all you need is a gold Xbox live membership and ODST. Once you have the opening screen when the beta comes out on the bottom it will have a little thing that asks you if you want to play the Halo: REach beta

if you play long enough on the beta a sign will pop up on the screen telling what to do.

You can buy and download the Mac beta client from the website. To run it just follow the on screen instructions.