I have a MySQL and Apache web server (both are installed on the same machine). Users will interact with it by a VB.NET application and the web. The server is accessible by the Internet.
The information is not super critical, it's just stats/benchmarks (especially since anyone in the world is allowed to view it)
These two statements seem to contradict each other. On one hand, both MySQL and Apache are on the same host, but "anyone in the world is allowed to view it." I'm assuming you're referring to the data output by your web application?
If the first statement is true and both your Apache webserver and your MySQL database server exist on the same machine, there is no benefit to adding SSL, as Raniz mentioned in his answer. However, if they exist on different machines or if you access MySQL remotely, you should enable SSL.
The important thing here is to model what SSL protects you against, which is primarily password-stealing. If you connect to a MySQL server over the internet without using SSL, anyone who is lucky enough to sit between you and your final destination (the MySQL server) can easily extract your username and password for MySQL. They can then do whatever they'd like with the user credentials they've extracted.
You seem unconcerned with this possibiltiy in saying "the information is not super critical," but you likely should be concerned with this possibility. What if an attacker deleted everything from the database? Or subtly injected erroneous data and destroyed your site's credibility? What if they were able to use an exploit in SQL to get a shell on your machine?
If, however, like you say that your MySQL server lives and is accessed only locally (never over WAN), you don't need SSL. If it's public facing or ever shares data over an insecure network, use SSL.
An alternative to using MySQL over SSL is using SSH port forwarding whenever you need to access MySQL remotely.
ssh -L 3306:localhost:3306 myhost.com
This will forward all traffic to the local port 3306 over SSH to the local port 3306 of myhost.com. This secures your credentials while still allowing access.
SSL in general isn't the easiest thing to set up, and MySQL is no exception. Still, if you need services to access MySQL over the network, SSL serves a much-needed purpose.