OP: glad you’re looking into getting started in USPSA competition. Like many other shooting disciplines, there are multiple divisions in which you can compete in depending on the type of gun you want to use.
Right now Carry Optics division is the most popular in USPSA, however it requires a pistol which is traditional DA/SA or striker fired. It does require a red dot optic to be mounted on the slide between the ejection port and rear of the slide (it cannot be frame mounted). Magazines can have extensions on them up to 141.25mm in overall length (approx 23+1 capacity), however no magwells or thumb-rackers are allowed. Everyone is scored minor PF, so 9mm is the most common caliber. The DA/SA Shadow 2 (Accu Shadow is allowed) fits into Carry Optics, but the TS2 does not since it is single-action only (SAO).
On May 1 USPSA is releasing a provisional division called Limited-Optics. It is patterned off Limited division which does allow SAO action guns as well as traditional DA/SA and striker-fired pistols, but with the inclusion of a slide mounted red dot. Limited-Optics allow a few more features than Carry Optics, which include thumb rackers, magwells, and skeletonized race-holsters. Mag capacity is the same as Carry Optics, it is scored minor PF only so 9mm will be the most common caliber. What is not allowed are frame-mounted optics, mags longer than 141.25mm, and compensators. Word on the street is Limited-Optics was released to allow 2011 and other double-stack 9mm SAO guns a place to compete. Time will tell how popular LO becomes. The TS2 that has the slide milled for an optic will fit nicely into Limited Optics.
Open division is the OG race gun division where many of the modifications NOT allowed in other divisions are permitted in Open. Such as compensators, frame mounted red dot optics, longer mags that go up to 171.25mm (i.e. approx 29+1 capacity). So if your Staccato has a compensator, Open is the only division it can compete in.
There are other non-optic divisions in USPSA such as Limited, Limited-10, Production, Single Stack, and Revolver, but it sounds like you are focusing on red dot optic divisions.
Good luck!