The fastest you can sample is limited by the ADC clock, which can be as fast as the main clock frequency divided by 2, or 8 MHz. Now, at that sampling frequency your results will not be accurate! In addition, the datasheet says the ADC clock should not exceed 1 MHz (I'm guessing results will just be ridiculously wrong beyond that point). The "recommended" ADC clock frequency to meet datasheet parameters is 200 kHz or less (many of the ADC parameters are specified at 200 kHz). Another parameter of note is the "input bandwidth", which has a typical specification of 38.5 kHz so (according to Nyquist's theorem) there's no information beyond 77 kHz of sampling (though it is beneficial to sample faster than that if your signal truly does have spectral content up to 38.5 kHz).
OK, so with that out of the way, let's say you settle on 200 kHz, that means you are sampling data every 5 microseconds. That's way too fast for serial. At the 230.4 kbps baud rate and 8 bits per sample (throwing away the 2 LSB's of the 10-bit sample) you could transmit 23040 samples per second (10 bits per 8-bit data packet over serial) if your code was 100% efficient. So there's no need to even think about the 200 kHz sampling frequency number.
Storing data has a similar tradeoff. Assuming you use an Arduino Mega with 8K of RAM, set aside 1k for the C stack and other stuff, you could store (7*1024)/200,000 = 35.8 milliseconds worth of data at 200 kHz sampling rate. If you want to store 8 seconds using 7k of RAM you will have to sample at 896 Hz.
Just some numbers to get you thinking.
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The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected