Basically you can upgrade SermonSpeaker and you will not loose any of your data at all. That's because the data is stored in the database, and an upgrade will mainly replace files on the harddisc.
However since it's a bigger upgrade I would still recommend to backup the database tables prior to the upgrade. Just to be safe.
You can do this with phpMyAdmin or any similar tool. There are even Joomla extensions which allow you to create backups or manage the database:
ArtAdminer
is one such tool,
Akeeba Backup
is another one.
After you have done the backup, you need to upgrade your installation up to SermonSpeaker 3.2.2. You need to do this step by step with the upgrade packages found here:
joomlacode.org/gf/project/sermon_speaker...&frs_package_id=3275
. Each upgrade package contains a readme which explains what you need to do. Please read those and follow the directions closely.
Unfortunately I can't tell you much more than what is written in this readme files, as those versions were released before I took over the project from Martin.
After you got your installation to 3.2.2 (or if you already have this version or a newer one) you can just install SermonSpeaker 3.4.3 found in the download section on this site directly with the Joomla installer and it will do everything for you.
The modules and plugins are much easier to upgrade, just install the newest one from this site. They do nothing at all with the data so this will be safe.