Serial TTL is ideal; that is what the Arduino (or any micro with UART) actually has built in. It means you don't need an RS-232 level shifter (such as MAX232 family).
I tend to lump all sources of error into the label 'noise'. This can be RF and audio frequency noise as most think of it, but also temperature, voltage, aging and anything else that causes error in the measurement.
Most ADCs will spec their total error as +/- 1/2 to 1 bit (some even more). This means that you need to ignore the least significant bit when comparing 2 values because the real value could be 1 bit higher or lower. Also pay attention to the test conditions; is it at 25C or from max temp to min temp? Does the error get worse when sampling faster? Does it need a certain settling time when you change channels?
The ADC reference is critically important. If you calibrate the system when the voltage is 5.00V and later it is 5.05V, all measurements will be 1% higher. If the voltage reference is noisy, for example because it is also power digital circuitry that is switching on and off, then you can take consecutive reading with the exact same input and get different results, or different readings depending on which outputs are on and off. This can be a significant source of error on the Arduino since the default reference is the main power supply for everything. Precision References http://de.mouser.com/Search/Refine.aspx?Keyword=precision+reference which supply only the ADC reference and the sensor will significantly reduce this source of error.
Silicon changes with temperature. Normally 'room temp' changes of +/- a few degrees are not a problem, but if you are trying to measure with extreme accuracy then even small temperature changes can be significant. That is one of the primary reasons laboratory scales say they should be turned on for 30 minutes before they are used. Some precision instruments use a heater to keep the critical circuitry (sensor, ADC & reference) at the same temperature all the time.
I'm sure you've had basic circuits and know RC filters. If you've had a filters / op-amp class then you will have seen some active filters. If you have had classes in sampling you will have heard of the Nyquist frequency Nyquist frequency - Wikipedia. If you use a single pole filter with a cutoff frequency of 1/2 your sample rate, it will not eliminate the higher frequencies, only attenuate them. You need a multiple pole filter and/or a cutoff frequency far lower than your sample rate. Ideally you want to filter the heck out of signal, but the R's and C's (and op-amps) will also be sensitive to all the sources of error, so it is a trade off.
The simple way to get around all this is to use the best components you can get, sample with higher resolution than the calculations say you need, over-sample and average to eliminate short term noise and then ignore a few least significant bits.
I think your best bet for this project is to use a commercial scale and read it via serial TTL, but...
If I had to do this, I would look on the websites for Analog Devices, Linear Technology, Burr-Brown etc and see if there are any reference designs and/or white papers for something similar. The maker of the loadcell should also have some tips and hopefully, reference designs.
If I had to do it all myself, I would want a load cell rated at least 2x my needed resolution (0.05g, preferably even better) with very low error specs, the best precision reference I could get and an 18 or 24 bit ADC. I would oversample 32x or more if there was time, sum the readings and then right-shift to get a 14 or 15 bit results. Then I would put a calibration weight on the scale and log continuous readings for a day or so to see what my max and min is. I would test it with the external power supply voltage at min and max and if possible, I would test it in a thermal chamber across slightly greater temperatures than would be expected. If no thermal chamber is available, I'd test it warm with a blow-dryer, space heater, black box in the sun etc. and I'd test it cool/cold in a refrigerator, outside or in front of an air-conditioner vent etc.
This assumes the accuracy is really needed. In my experience people will tell you they need a lot more accuracy than they are willing to pay for. In a laboratory situation the researchers may have thought about what they need, but it may be even more likely they are asking for higher precision because the last they want is to publish a paper and then find out their great discovery was all just a figment of poor measurement.
Good luck,
Steve