Updating Joomla

I have Joomla3-3.4.6 installed on FreeBSD 10.2-RELEASE.

What is the preferred method of keeping this up to date? Usually with my other ports I wait until the port is updated, however my web developer is pushing me to update to 3.6.2 which isn't available in the ports yet.

He said I should use Joomla's own update mechanism.

I'm not sure I want to update in this way, but if that is how the majority are keeping it up to date then I'll give it a go.

Use Joomla's own update mechanism. I do it all the time with no issues. However, always backup the database and files before doing Joomla updates. Sometimes it'll break the plugins or template you're using. Always do the backup so you can roll back if something breaks.