As soon as you can afford to do it is the best time to start.
My mod recommendations, in order:
0) The Driver Mod* – this mod outweighs all others put together (my 2¢, of course)
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1) Uprated Brake Fluid and Brake Pads
2) Tires – ones that will hold up to track abuse and still be safe when it's raining while street driving
3) Schroth Quick Fit Pro 4-Point Harnesses
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4) Limited Slip Differential
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5) Camber Plates – or whatever means you choose to achieve a street/track alignment in front
6) A Street/Track Alignment – one that pretty much ignores tire wear on the street (e.g., the tires may last only 8-10K)
Forget the go-fast bits; they make no difference in the corners (where the fun is), and the car is more than fast enough on the straights. Learning to drive well is job one.
My list is oriented towards reducing the time between starting tracking and becoming the kind of driver who can get more than 75-80% out of his car as-built.
If you really want to shrink that time frame, hire a professional race car driver to coach you after you've done 10-20 events.
Be prepared to burn your brakes down. To see what that means, search for threads with statements like "why are my calipers this ugly green-brown color?". If you can swing it, drive with a club that has instructors who can help prevent you from doing that. Learning and applying correct braking techniques will make you faster and safer than just about anything else on a race track. Those techniques are radically different than anything you're used to doing on the street.
In that vein, I recommend focusing on events where instructing novice and intermediate drivers is taken seriously. Many events are not well-organized to develop novice and intermediate drivers. I recommend events sponsored by BMWCCA chapters in your region (
https://www.bmwcca.org/chapter/finder), NASA (
http://www.drivenasafl.com/), and Chin Track Days (
https://chintrackdays.com/).
* The driver mod entails doing everything you can to become a better driver: listening to your instructors, trying autocross to see if you like it, driving any car control clinics that may be offered in your area, and studying the craft (there's quite a bit of free information at these two sites:
https://speedsecrets.com/ and
http://www.peterkrause.net/Krause_%2...C/Welcome.html).