First, be realistic. 2000 GSR makes around 150-155whp BONE STOCK. With $3000 you can get to 190whp pretty easily with small mods. mid 200s is impossible unless you want to spend $10K-15K on a build engine, dyno time, etc.
REALISTICALLY, for $3000 your looking at a setup i just recently did :
Skunk2 Stage 1s-$500
Mr. Kidd/Batlground Header-$400
Skunk2 Intake manifold $200
AEM Intake $250
Crome Pro ECU and Harness-$270
Skunk2 Mega Power R Exhaust-$450
PARTS-$2070
The extra money would get you install and tuning an you would make about what this customer makes:
http://batlground.com/gallery/thumbnails.php?album=195
So you wold pick up about 40whp and 15-20TQ. the car would feel totally different, much faster than what you have.
Now you could do a QUALITY turbo kit for around $4500, make 220-230whp/180-190TQ and be much faster, but it does cost more.