There are two things to check/do before upgrading from 3.0.19.x.
1. Back up your database. There are a lot of plugins that can do this. I use WP DB Backup. Having a backup of the database means you can go back to the way your site was before if something goes awry.
2. Make sure you do not have any currently active events. The issues we have had reported from earlier versions of Event Espresso have all been surrounding attendee data and payment information. We have not been able to reproduce the problems on our test servers, but we are handling and calling some data differently in the newer versions of the plugin, so the problems that were reported were around those areas.
If you have any questions or problems, then please create a support post in our support forums so we can help you.