Best way to show a lot of video on my website (streaming site)

I'm working on my streaming site. I have 2 questions regarding videos:

1) What is the best format to upload video in my site? I tried MOV and it was incredibly slow... so which format do I have to use? Mp4? M4V? MPEG? H.264? AVI? ... (ps: I can put them on youtube then send the link on my site because its a premium content)

2) Which plugin (player) you recommend. There is hundred of them. I'm willing to pay for. I just need to know witch on are ideal for a website that stream HD video course online.

On last thing, do you have any others advice to give me about the speed? I fuss a playing a lot of video can slow my site? I hope not. Thank you for your time and help.

Best regards,