Drivetrain 97 GT gear install halfway through

Hello friends. So this will be my first real post on the forum and I’ll just let u know it’s all inspired from the stickied modification survey thread. So here goes.
I’ve got a 97 GT that I got at an auction for $900. It came with a k n n intake, not sure what kinda exhaust but it’s aftermarket, 20” rims and a pretty bangin flip out touch screen deck.
I’ve been reading the articles here and watching vids on YouTube and waiting for my packages to arrive so I can really do some cool to my car. I started the other night with some adjustable airstruts in the back cuz I also have 3” wheelspacers back there cuz I hate how it looks with the tires all tucked under. Anyways 3” may have been a little much but I love how it looks and the air shocks are doing an awesome job of keeping my tires off the fender.
Next and probably the best mod is gears. I’m halfway done and am gonna lay my situation out here now and let u know how it turns out. I’m a pretty bangin mechanic so I’m not sweatin anything too much but I just wanted to talk about how there were no shims on either side of my diff when it came out. And I’m not sure but I’m thinking that’s why there was about a quarter tire rotation worth of backlash prior to this project. It was really ridiculous. So now if anyone with some knowledge on this can chime in before I get back to work I’m just wondering if there’s a recommended shim measurement I should just throw in there to start with. Cuz I’m for sure putting something in there to kill that backlash I just am wondering about a ballpark estimate of where to start.
In the event that I cannot wait any more and just get back to it I’ll post what I do and how it goes. Thanks in advance and thank u to all those who wrote gear install articles etc etc and I’m out.

Thanks for ur replies guys. The gears I pulled out were 3.27. I put in excel 3.89. There were these weird rings that almost looked ceramic where shims would have been. I tried reusing those but on one side it broke when I was hammering in the ring assembly. So I stacked up some shims about .15 less than the ring I broke and put that an the right side and used the ring that didn’t break on the left side. That gave me zero backlash which I thought was a good thing. Found out the hard way it’s not. So tomorrow I guess I’m gonna open er back up and remove a little bit more shim so as not to have to hammer it in. Another thing I thought was a good thing. Did not know it was ok for it to just slide in. Thanks again for the replies and I will post with next results. Also have a transgo shift reprogrammer to put in after the gears are right.