A handheld like the TDS3 is more precise, while some think an inline is more convenient. We are a sponsor and Master Distributor for HM Digital - we carry two different handhelds and two different inline meters, as well as calibration fluid.
if you're using the handheld one, could the container you're holding the water in contaminate your readings? versus the inline one directly measuring pure water from the unit?
Sure - you could manage to get bad readings from a handheld. To aboid that, use a clean (as in right out of the dishwasher) glass sample container (drinking glass) and triple rinse with the water you want to measure.