Lets talk Autocross

Are you saying no front sway bar right now, or just the stock one?
Honestly, even without, you'll still have fun at the MATS autocross. But if your going to take a school (I added Evo School link above), you'll get more out of it with a front sway bar. Do not add a rear sway bar until you've added a front sway bar, specifically a large aftermarket front bar.

Shocks. Nowadays there's a lot more options. Just run what you have until you're ready to buy (unless they are not working or making you unhappy). Just don't waste your money on KYBs - especially on a street cruiser. Not enough high frequency damping. Although on a full rubber suspension maybe it wont be so noticible.

Oh. There is one possible issue. The typical power steering pumps can't keep up. I dont know the details as I use a manual box. Steve Wall can fill you in on that if it doesnt show up in a search.

One more. I like to run a fairly full fuel tank. Keeps weight from sloshing around and puts weight where its needed.

Currently I don't have any sway bars

Funny you mentioned the power steering pump. I remember back in high school sliding My early "A" Mopar around in the rain and having problems with the power steering getting hard and losing power intermittently. It was the old style pump with the large cap. This Dart I think has the saginaw pump and box out of a 74 Valiant I also put in the washer to lower the pressure in the pump a little.