Welcome to the addiction!
The tips by khaosman (as well as the threads he quoted) are very good. Definetely figure out which class you would like to enter, and let that guide you w.r.t. mods, tires, etc.
Just in case you want to avoid the cost of new rims, here is another idea: consider installing new Falken RT/615s on your stock/OEM rims. I had a set of 205/40R16s mounted on my MP5 throughout the spring/summer/fall of this year. They worked worked well during the occasional practice, as well as for daily summer driving. They do make your car look funny (very short sidewalls, very big wheel wells, stock ride height), will lower your gas mileage, and will ride a bit rougher than taller-sidewalled tires. They worked well in the rain (no standing water), but I would not want to drive them in snow.
The shorter sidewall gave me a bit of gearing benefit, so the car would feel a bit more responsive during acceleration, as well as quick steering response. Overall, I really liked them.
(I just replaced them last month with a set of M+S tires for the winter. I will re-mount them when summer gets here.)
I would think the 215/45R16s would work well well on stock rims (16"x6"), and would probably be a bit more practical in day-to-day driving.
Replacing your daily-driver tires with Azenis (or Hankooks) may work well for an initial dip into Autocrossing. If anything, you can always buy the tires now, and swap them to a new set of rims if/when you get those.
Good luck.
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