Serial.write() doesn't seem to be fast enough, since it takes 1, 2, sometimes even 3 ms to do the sending.
At what baud rate?
I see there is a Wire library; could that be solution to my problems?
The Wire library is for I2C communication between two devices that support I2C. Does your PC?
problem is Arduino's built-in memory isn't big enough
There are external EEPROM chips that you could use.
so maybe Icould write everything on an SD. would that be fast enough?
Depends on the code. Buffering the data and writing it in large chunks, each time you open the file is faster than opening the file, writing a value, and closing the file.