You will bring your bank account and vehicles (the ones you've retained) to the co-op game you join. The progress of the server depends on the host. If you host, it will continue your singleplayer game. Trailers that you purchase on another person's server will disappear when you disconnect. I'm pretty sure you get refunded for those trailers when you disconnect.
Any progress you make while playing in somebody else's server will not count toward your singleplayer progression. If you find a free truck in the world, only the host gets to keep that vehicle. You'll have to find and acquire the truck in singleplayer or you'd have to be host in order to keep the vehicle.