I'm very new to arduino. I would like to make a project where I can read digital 8bit data from a circuit and store it in the board and then send it via bluetooth to an android phone/computer.

I'm not sure which board to choose and what to use for bluetooth communication.

You need to supply much more detail

I can read digital 8bit data from a circuit

What circuit, how is this data read?
What speed is it coming at you?
How much do you need to store?
What rate do you need to sent it on with bluetooth?

This is for a monitoring system where 8bit data from each IC unit represents different information. The 8bit data along with header is read and interpreted in a computer/phone using JAVA.

The data comes from 8bit IC units (say 4units) whose clock (output) is controlled by a decoder (2:4). Output is continuous if clock is continuous.

All outputs are connected to the same 8bit port. The decoder selects which IC’s data is read at the port.

For first unit say binary 00 is sent to the decoder by the arduino which selects first unit.
01 for second unit
10 for third and
11 for fourth
That’s an example with 4 Banks. Storing is not so necessary as the data is read continuously, sent and it appears in the Bluetooth device in Real-Time.
The data must be read in a loop continuously and sent via Bluetooth. Based on Seeedstudio Bluetooth Bee (which I would probably use) the baud rate of Bluetooth would be 38400.

I don’t know much about the arduino but in a Microcontroller, I would set PORT 1 to 00000010 (10 => 3rd unit) connected to decoder whose output would be 0100, where 3rd pin connected to clock of 3rd IC unit. Then read data from PORT 0. From there send it via Bluetooth with the header saying which IC unit it is 3. (Don’t know how I would do the bluetooth part yet)

Something like

#include<REG51.h>
int i;
void main(){
P0 = 0;
P1 = 0;
while(1){
for(i=0;i<4;i++)
{
if(i==0) {
P1 = 0x00;
// P0 now holds data from 1st unit which is to be sent to the Bluetooth device
R0 = P0; //store 8bit data in Registry Bank 0 and then perform bluetooth transfer
delay(100); //make sure data is sent (not sure what the delay is. depends on speed of the bluetooth device)
}
if(i==1) {
P1 = 0x01;
// P0 now holds data from 2nd unit
R1 = P0; //store 8bit data in Registry Bank 1
delay(100);
}
and so on…
}
}

Also what if data has to be sent to computer and phone simultaneously.

I want 8bit data read by the Arduino and send it to bluetooth enabled device.

The 8 bit data comes from 8bit IC's whose clock is controlled by the Arduino.

Once data is read, it needs to be sent to the Bluetooth device.

How can I go ahead with this?

Is it 8bit serial data, or are there 8 data lines?

Its 8bit lines (parallel) not serial.

Reading 8 bits of data is best done using a port expander.
An MCP23S17 is a good one, you get two 8 bit ports in one chip and 8 chips can easily be connected to the same SPI bus without any extra address decoding. So that is 16 ports. If you want more then supply separate chip enable signals to groups of 8 chips.