OK, it's all good.
Back on topic, just about everything that I would advise has already been said:
Keep an eye on the Events section of SAU and any other forums you might be signed up to, there are quite a few track days around, both out on the track on your own, or with instructors.
If you want even more options, get yourself a CAMS or AASA licence (CAMS requires you be a financial member of a car club such as SAU, but it is accepted in a lot more places)
Kudos to you for doing the right thing and keeping your racing OFF the streets! As Nathaniel said, if you can convince others to do the same, then we can all rest a little bit easier and it might help to change people's attitudes towards all of us enthusiasts, no matter what we drive.
And there is absolutely nothing wrong with a Mazda3 Neo - I drive one fairly often, and it's an awesome little car! Just make sure you get some grippy tyres on it.