Your friend's suggestion is spot-on, autocross is probably the absolute best way to learn performance driving because it's low-cost, low-risk, and a ton of fun to boot- you'll learn a lot. What part of the country (/world) do you live? Most of the North is in hiatus until the spring, but a lot of the south have year-round autocrossing. Someone here may know offhand, but if you google "autocross" and your local area, it should pop up your local SCCA region, PCA region or other indie clubs. It's amazing how good these cars really are, especially with good tires and a performance alignment. A lot of clubs have autocross schools/cone clinics and/or test & tunes in the spring, either of which will give you a lot of seat time. You can also look for Evolution or Solo Pro driving schools which cost more than club clinics, but have professional instruction. HPDEs and other track events are great, too, though there is higher cost and higher risk on the track than compared to autocross; the plus is that you get a ton of good seat time (with an instructor) during an HPDE.
I have a 2004 Boxster S I daily drove for 6 years and my wife and I both heavily autocrossed and frequently time-trialed. It's great bone-stock, though you may find you need to renew the bushings and all just from age. The only mod I made to mine was a GT3 front swaybar which helped tune the handling (and counterintuitively- decrease understeer). You'll want to get a performance alignment. But I wouldn't change a thing right now, not until you drive it a few months and a few autocrosses and get a point of reference.
If you're on OEM 17" wheels, I recommend Bridgestone RE-71R tires in 225/45R17 & 255/40R17 sizes (little wider in the front than OEM). They're the best autocross tires right now, great street tires, and really good on the track, too. The biggest "con" is that they wear quick. You'll need to be careful you don't end up with an alignment that chews tires. Dunlop ZII Star Spec are fantastic tires as well- they were, arguably, the best tire for autocross 8 months ago until RE-71R came out and aren't quite as fast, but they'll last probably 50% longer. Both handle very similarly and you're not likely to notice the difference in speed at this point if your development as a driver, though you may regret the slower tire the first time you lose by a tenth of a second, lol.