RX7 for £4k will be a sh*t bag imo
And skyline is nice, but remember parts and servicing can be pricy for any non uk model car. Especially if your dealing with some locally to repair it and they have to order the parts in for you.
If it dont have to be Jap, and your not fussed about money to repair, then consider an A4 (B5) 1.8T or T Sport, you can chip tune them to 200bhp for a couple of hundred quid, sleeper looks , german power, doesnt come with the sh*tty bmw reputation, or even a newer model if you can find one, although i dont know if 4k will be enough for one of those. And repairs not that bad, they are rare to find now in low mileage but if you have a few weeks and you look you will find one with history. Also i dont like the newer model i think the B5 had character.
I replaced cam belt about £250 at Audi, clutch was about the same price, i owned it over 2 years, apart from those items it flew through the mots.
Also, BMW, you can get an E36 i think, go for a 323i again a lot of power to play with and refinement /german tech, has a reputation but hell i wouldnt care its a lovely car
But your moving into the gas guzzlers though.
Can also consider a Golf mk4 gti turbo , Seat Leon 1.8 t, Skoda Octavia (i think) 1.8T / RS, all the same engine as the Audi all can be chip tuned right off the bat, providing engine is solid and it has history. Bang for the buck its the easiest way to get a good bhp increase, and they can be switchable to, leave as a sleeper and no one will know any different