Tires are the first performance upgrade I plan on making for my car sometime during next season - the Falken Azenis. Take it from someone who just began this season, after my last two events of the year, all I wanted to spend my money on was a new set of tires.
To stay stock (as listed above), make sure to stay on factory sized rims. Since you're on the ZX3 model, you can go for the larger sized rim offered on the car, which is 16" I believe to still stay in HS.
I totally agree with Carrera. There's no point in pooring money into modifications on a car when you haven't even experienced it out on the course. You'll be making changes to the car without knowing what you really need to do, especially if you intend for you modifications to make you more competitive for autocross.
For the most part, it's your driving that needs the upgrade and not the car as stated. Stay stock for now, save your money, and then spend accordingly after getting to know your car better.