For 6k your not going to get a good VR4 or 300ZXT.
You can find early 325i bimmers for $4,XXX its not to hard around here. However a 328i is going to cost you. I would really think about a E30 325i between the years 89-91. They run like mid to high 15s in the 1/4 mile. You can get a nice one for around $3,xxx or one that needs a little work for less. Then with the other 3k you can make it REALLY fast. They turbo well and it dosnt take a lot of hp to get them fast. The best example I can think of right now is a guy on E30tech.com that ran a 12.1 on street tires with 270whp. I wouldnt call them money pits BUT if your broke a bimmer might not be the car for you. When you first pick up these older E30 there tends to be a lot of little things you got to fix.
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Lindsey Boost Enhancer, Blitz EBC, Hot Air Intake, Koni Yellows