How do you transfer plugins and the plugins data to another site?

I've re-designed a site and need to transfer plugins from the old site to the new site. I'm not sure how the plugin stores data, but I'd imagine its in the folder of the plugin itself. Am I wrong?

Anyhow, would I just move the whole plugin file from one server to another? Say it's the plugin Ultimate Membership Pro which stores user info, tracks sales, etc... Will that data transfer if I just transfer the plugin folder from wp-content>plugins to the other server.

Thanks in advance.

use a wp backup program then put it back to the new wp.

i see that as the best idea.