I really wouldn't recommend starting the players in TIE fighters. Aturi relies on the AI having similar or greater numbers of ships to limit the gaming of its AI system. To make good use of the Aturi system you really don't want to invert that.
For the sake of this, let's rank the Imperial and Rebel ships into four power tiers.
Tier 1: Z-95 Headhunter
Tier 2: A-wing, HWK-290
Tier 3: X-wing, Y-wing, B-wing
Tier 4: T-70, E-wing
Tier 1: TIE fighter
Tier 2: TIE/fo, TIE advanced v1, very basic TIE interceptor
Tier 3: TIE interceptor with basic upgrades (built in Autothrusters for example), loaded TIE bomber, TIE advanced x1 with title
Tier 4: Loaded TIE punisher, TIE defender, TIE phantom
Aturi pits Tier 3 (X-wing, Y-wing, B-wing) and buffed Tier 2 (A-wing, HWK) against Tier 1 Imperial ships. This means that even if the Rebels are relying on Z-95s you're going to be using Tier 3 or buffed Tier 2.
If you want the Aturi dynamic to work with large numbers of X-wings instead of fighting large numbers of Z-95s, you'll need Tier 4.
This is probably going to work best with the TIE interceptor, TIE advanced and TIE bomber as your starter ships, and if you want the Rebels to put in a proper showing you'll probably need to bring in the Fourth Tier of Imperial ships.
But keeping the Imperials in TIE fighters is going to require either enough ships to break the system or some crazy high levels of TIE fighter upgrading.