For example, if you've recently synthesized a previously-unknown chiral compound, and want to measure it's optical rotation, what factors go into determining the solvent, cell size, wavelength, etc? Or does it much matter provided everything is reported?
It doesn't matter provided everything is reported. However, it is convention to measure optical rotation at a concentration around 1 g/100 mL in chloroform at 20 or 25 °C using a sodium lamp (589 nm). I've only ever encountered cells with a path length of 1 dm.
"provided everything is reported" is absolutely critical. Any measurement of optical rotation should include solvent, temperature, and wavelength.
There are some experimental considerations though, that can be helpful. I'm not so sure about a "convention" of using chloroform as a solvent - it seems to me that almost all of the rotations I've seen were run in methanol, but that might have been just because of the places I worked.
If you have a strongly colored or dark solution, it might be difficult to get a good reading using a 1 dm cell length at 1g/100 ml. Also, many compounds of interest aren't that highly soluble, and a compound that isn't completely dissolved will give incorrect measurements. For those cases, you can either reduce concentrations or use a shorter cell (they are available for many of the newer polarimeters). The cell path length is very carefully measured by the manufacturer and is usually etched into the side of the cell, to three or four significant digits.
Also, a polarimeter will only read from +180 to -180 degrees, for reasons which should be obvious and are left to the student to explain. It is good practice, although rarely done in any of the labs I've been in, to take optical rotation measurements at two different concentrations to make sure you don't have a very strongly rotating compound. And sometimes you will have a compound that has such a small rotation that it is very difficult to measure accurately. In these cases, if you cannot increase the concentration sufficiently to get an accurate measurement, you can sometimes get a stronger rotation by changing the wavelength of light. Most polarimeters now have at least two lamps, sodium and mercury, or a tunable laser so you have a selection of wavelengths to choose from. This can make comparisons to literature values somewhat troublesome - although you can calculate a standard rotations based on concentration and path length, I don't know of any calculation to standardize rotation based on wavelength.