Moving site to different server and database

Hello poeple,
I am new with wordpress and on this forum.
Please forgive my bad english in writing.
I normaly work with joomla but recently I started working with wordpress for some of my websites because it has some features which are perfect for some of my sites.
Like the apps for ios, android ans so on.
This makes it easier for some of my clients to work on their sites.

So my question.
I always build my sites inside my own computer using a usb server.
With joomla it was the easiest thing to do to migrate a site from my computer to a remote server.
Akeeba backup and kickstart made it childsplay.

I tried some of the plugins from wordpress but not with big succes.
My question is wich plugin is the best to use to migrate and if possible a free one because I work for non profit orgs. And they are not rich.

Thank you for all reactions on this forum, wkr jack holland