I want to play the campaign and coop with random people, but I would like to be the host.
With no filter, I always join in available coop servers which may have high ping for me.
How can I be the host and let others join my game?
I have tried public in the case above, and private, but no one in the community join.
Thanks.

I don't think there is a way to force yourself as Host on the 360. If you are playing on the 360 your best bet is to do what you are already doing. According to Bethesda's recent http://bethblog.com/index.php/2011/05/20/brink-%E2%80%93-an-update-on-updates/, your game can lag even if it's the other players who have bad ping. If you aren't already doing so, choose a specific mission. That should increase your chances of being the host. You may have to play with just bots for a few tries before the mission starts to fill up. Then just wait after completion for the next mission, it will autostart, and should take co-op randoms with you.