Also, OP.
You mentioned that you want to get into Autocross. ....be aware and please actually understand that as soon as you start down this path (nothing wrong with it), your reasonable "$20k used GTI" is eventually going to cost you at least $8k in parts and labor and tunes, because it is a GTI and that is what you are going to do; and up to $12k when you start including the more frequent, expensive oil changes and brake replacements over the life of this thing. You just are. believe me. I have little to no interest in such things....but I convinced myself to get a GTI because maybe I do have such an interest....maybe. I have no interest in modding the car, because it's pretty decent stock....but maybe I do? maybe...Yes. I am convincing myself they I need a new FMIC, a new downpipe and eventually a new stage 1 clutch. Yes, this is all stupid because I don't need any of it. My brain is working against me, though. Luckily, I spent the fun money on the car already so I really can't shit it away any more.
however: you will get new performance tires, and you will very likely get new, lighter, possibly wider and/or taller wheels. It's the thing that you have to get with a GTI, because the stock tire options are garbage. That's a default $1k on top of whatever you pay for it. You will lower the car because you don't like the gap in the wheel wells. All those baller dudes on Reddit have done fancy things to their cars. You are going to need new springs....who cares if you ruin the great adaptive chassis control tuning on your car, if you get one with DCC, you're going to do it anyway. You're going to get plasti-dipped VW logos, and black badges to replace the red badges. You're going to get a spoiler to stick on top of the stock spoiler, because it needs more rice. You're going to get carbon-fiber mirror caps and euro-style adaptive front and rear lighting packages because the US version sucks.
You're going to prowl EBay and international parts distributors for either Euro GTI rear seat headrests (low profile), or US Audi A4B7 headreasts (Same fit), because the US high profile rear headrests are unacceptable! And when you can't find a good used Audi set on Ebay for ~$40, you will convince yourself that a set from Europe, ~$270, is quite a reasonable expense...Hey, it even has the red stitching!
You are going to prowl deAutoLED to find bomb interior lighting options like underwell red lighting and brighter trunk lighting packages and such, because man is it cool. You are going to replace your stock air intake with an IE or APR one with fancy carbon fiber detailing and improves performance....exactly zero but hey the engine bay looks cooler and it sounds a little neater and oh man, carbon fiber! You're going to swap out at least 2 rear sway bars. You're going to decide that you should have replaced the end-links the first time, which means you will have to perform this service at least 3 times.
.....owning a GTI is something of a disease. It's willfully engaging in a large, uncured illness that many just accept and have no reasonable plan to cure in themselves. You can fight it as long as you want, but the only way to fix it is to drive the car into a ditch or sell it for a Hyundai. There is a strong community for those with this disease, but none of them are seeking a cure.
....by the way, have you even considered the Veloster N? I highly doubt you could get one at $20k (probably have to pay ~25-27k for one, which would be great deals). It is supposedly much better to drive, it's far ricier and it farts a lot. Kinda garbage on the inside, but it's a fan favorite....and think about it this way: you are spending at least $5k more on your GTI. Without question. That is what you will do. Veloster N is more track-ready at stock than is the GTI.
It's also a car (back to GTI) that I would be more hesitant to buy used. You have no idea how that car was driven, but most likely it was rough, and not always in a good way. You should really only consider 2018-2019 models, because they come with the 6 year/75k warranty, that is only available with those model year VWs--it has already been discontinued with 2020 and forward VW toys.