The turbo in your car should be a Borg Warner KP-39.
If you are at all interested in allowing for future power upgrades, you could install this, which is cheaper:
https://www.idparts.com/garrett-vnt-17-turbocharger-a4-bew-p-761.html
If you want to keep your EGR system functional, make sure to select the check-box to add the EGR cooler pipe for $60. It's a bit longer than the stock one and is required when switching to the VNT-17 turbo.
So combined, those cost $859.
To get the original stock turbo is $929
https://www.idparts.com/borg-warner-kp39-turbocharger-a4-bew-p-1332.html
The VNT-17 is a "stock" turbo for the 150HP European version of your car, so it just bolts right in, other than the need for switching that EGR pipe.
Once you have the VNT-17, you can run it with a stock car, or, you can add a 3 Bar MAP sensor for about $40 or so, and then get a performance tune to increase your power to about 170 HP. You'd need a new clutch to support that though...so that gets expensive.
If you just want to use it in the stock configuration, the VNT-17 will probably outlast the original KP-39 because it's a lot bigger and won't be working as hard.
There would be a small amount of extra lag with the VNT-17, unless you get the car tuned, but it's not too bad. I do have a tune, but I've also driven with that turbo on the stock programming and it's fine.