Look for the lowest combination of purchase price, insurance premiums, and repair costs. It's better to pay a little more for a car that will cost you less in insurance & repairs - but consider both any repairs it needs now, and the cost of consumables(tires, brakes, etc.) and routine service(timing belt, water pump, etc.).
Also, what ever you buy it will need work at some point.
I have no clue about Motorsports in Germany or the EU(other than people driving the Nurburgring), so I can't give you any advice there.
Warning: I have nothing constructive to add.
From what I understand, when it comes to doing things in Germany it's like a mix of being a Jeep owner (Just Empty Every Pocket) in Britain (oy, you got a permit for that permit application guvnahh). I have no idea what the motorsporting world is like in Germany but I can only imagine that it is heavily uber regulated and very expensive.
How much driving have you done so far?
Have you looked into kart tracks nearby?
I think maybe try renting a kart every other month or so might satisfy your need for speed until you have more money or a nice paying job. That way you also don't have a machine to maintain. If kart renting is affordable, you can spend the money on a good helmet and suit. Once you learn some racecraft, you can take your suit and helmet with you anywhere, and finally drive the kart track in Seoul.
If you get a car, you're going to want to change parts and tune it, which will wreck your budget and study time.
Thought I remembered your drivers license thread, and I was right. For those who missed it or might be interested https://grassrootsmotorsports.com/forum/grm/getting-drivers-license-in-south-korea/161480/page1/
I don't know anything about motor sports in Germany. Have you investigated joining with a "team" of some sorts? Visited the closest autocross events or a track perhaps? Does your school have a team in the university competitions?
I have no idea about Germany (all my German friends moved to the US or Austria), but I know motorcycles are significantly cheaper to run in the UK than cars are.
Other advice: find some race team that needs help, volunteer in exchange for seat time while learning everything you can.
Not super constructive also:
The odds are stacked against you right now. I don't think its the right time or situation to own a car. It seems like your budget is scratching the absolute minimum it will take to get an operational vehicle insured and on the road. You are a few entry fees or one broken part (which will happen) from being broke. Racing cars is a brutally expensive hobby, even in the US where auto ownership is significantly cheaper.
Consider some alternatives:
A) Karting @ your local kart track. There are competitive leagues you can join at many of them and the costs will be way, way, way lower, and much lower financial risk & time commitment. As you are probably aware, this seat time translates really well into other forms of racing should you head down that path later. Many times karting also offers a lot of other bonuses over entry level racing: Wheel to wheel, enduro events(!) - these are tons of fun, weekly competition schedules, etc.
B) Co-driving. Not sure how this works there with license and whatnot. At an autocross here, co-driving is both super common, and a very good way to improve as a driver. You can work out an arrangement with the vehicle owner to help out with entry fees, work on the car, buy a set of tires, etc.
C) PC Sim racing. You can build a solid setup for 1/2 your budget and have all the competition & virtual seat time you could ever want. Sure it isn't quite the real thing, but it may satisfy your desire for competition.
On the subject of actual cars: If you want to do autox or track events, many of the hatchbacks you have shown are a set of sticky tires away from ending up on their roof. In general in the US if the rollover info is not published, a car is not legal to run if the track width is not wider than the height. Sometimes exceptions are made, but you don't have to look hard to find videos of cars on 2 wheels or rolling over.
On the subject of tires: Check your local racing organizations rules. In the US there are basically 3 tire classes: 200TW, R Comps, and Slicks (not street legal). 200TW is the most accessible and very common now. Generally the smallest size you will find available here is a 23" tire on a 15" wheel. Not sure what is available over there. Beware, they will be quite expensive compared with the tires you have shown above. And trust me, racing with the wrong tire for the class is not fun. Also, in general, the wrong tire won't last any longer than a 200TW tire, so don't talk yourself into a 500TW tire thinking you will save money.
Isn't getting a license in Germany pretty expensive to begin with? Like half your budget expensive? Hopefully someone can chime in with more useful specifics.
Like you, I’ve had the itch to race wheel to wheel for a long time. Life hasn’t let me have the spare money or time but I have found that it’s a lot of fun to be involved in other ways, stuff like working at a track or crewing with a team.
For me it’s doing pit crew stuff with a ChampCar Endurance Series team. Not quite the same as driving, but I get to hang out at the track, be part of the team, do racecar stuff, learn a lot, and make connections in the racing world. All without having to spend the time and money to field my own car.
I think people have the right recommendation w/karting.
Find a karting center that has 125cc competition and isn't just a rental fun/entertainment center. They should be able to get you headed in the right direction.
Here is a video series from a few gentlemen that race a Citroen C1 in a race series in England. They break down their whole build and explain out everything needed. Seems for a basic race series a very easy way to get into competitive racing along with a cheap running vehicle.
https://www.youtube.com/watch?v=OkoCuKOSpeo
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