One important question - do you have to register the car in Germany as a regular resident, or are you able to register it under exemptions like they at least used to have for US military? That makes a massive difference to the recommendation.
Skylines (and Elises etc) aren't exactly common in Germany, at least not compared to the UK and Ireland. While it's easier to register a car in Germany that's been registered previously in the UK or Ireland, it still requires jumping through a bunch of hoops that I wouldn't recommend to anybody not familiar with the process[1], especially if you don't speak fluent German. You can probably find a Skyline that is already registered, though. Same goes for Pulsar Gti-Rs and BG chassis GT-Rs - much more common in the UK, not very sought after in Germany.
Therefore, I would recommend sticking with cars that are already registered in Germany and still have valid TÜV and WhateverTheHeckTheirEmissionTestIsCalledTheseDays. Also, keep in mind that while it is possible to modify cars in Germany, any modification has to be listed in the KFZ-Schein (equivalent of a US registration doc) and the KFZ-Brief (equivalent of the title). If they aren't, that can get expensive. BTW, that can go down all the way to the tire size (normal) and tire brand/tire model you're allowed to use on the car. Oh, and of course wheels, suspension, body modifications, seats, exhaust, air filter etc etc etc. Imagine the CA DMV on a particular sadistic day, then double the pain .
Also, keep in mind that they do throw salt on the roads in Germany (more or less, depending on where you live) so a lot of German car people keep their nice cars tucked away for the winter. Kinda like we do here if you live the rust belt. If you buy something special, keep that in mind.
Anyway, some of my suggestions:
Matra Murena:
You might just about be able to find an Alpine A610 in your budget:
A Golf Rallye might also just about fit your budget, but like all the other cars above, not that easy to find:
One of these little guys should also be pretty easy to find:
One of these Renault R5 Turbos should be well within your budget in superb condition:
This one, not so much :
More French hot hatch goodness, Peugeot 205 GTI - flimsy, but boy do they go:
Got to have at least one Italian hot hatch - Alfa 33:
Or the original Alfasud, if you can find one that you don't have to carry home in a shopping bag:
Or if you want RWD and have watched too many European hillclimb videos on the 'tube - Opel Kadett C Coupe GT-E:
[1] I am German, but haven't lived there for a long time. When I moved from the UK to the US, I sold a bunch of vehicles to people from Germany who were importing them to Germany. IIRC in the case of my S1 Elise, it took the new owner a several months to complete all the required modifications to the car and register it. And that guy was a local who'd done this before. Of course he could have hired someone to do the work and potentially complete it faster.