In regards to the vna - I have no experience with the NanoVNA itself but have lots of experience with HP/Agilant lab VNA's so, in general:
1) Pick the smallest swath of spectrum possible - don't try to measure from DC to daylight in one fell swoop; in your case, though more work, best to measure at just the basic LMR bands of interest plus the civil and mil air bands if need be with SEPARATE individual runs - one of for 30 to 50 MHz, another for 138 to 174 MHz, etc.;
2) ALWAYS calibrate to a lab standard (or as close to as possible) open, short, through (assuming a 2 port device, if only single port, as in your case, you can omit the through standard), and load relative to the measure point from the VNA; so, if using cables between the VNA and the DUT (Device Under Test) make sure to calibrate out to the end of those cables before each new frequency range run;
3) As was mentioned try to use a resolution that works best for the kind of results you are graphing BUT if some results are really causing the graph to "squash" the bulk of the data (say an area of really bad SWR) you may have to break the test frequency range up into smaller segments to get readable and usable results.
Also, when dealing with unavoidable lengths of cable attached to the DUT and you have no equivalent DUT standards to use (as in your case) there is a rough workaround that isn't super accurate but may yield close enough ok results if used properly -
Port extensions - basically, if your VNA has this it kind of allows the ability to input a compensation that essentially "extends" the test leads out to the DUT. It CAN be pretty accurate IF all of the details of the coaxial test leads used are known, not just the length and the characteristic impedance but also the loss at the range of interest, velocity factor, etc. The more details the better of course also depending on what your VNA can accept as input compensation factors. This is where the "fudgy" approximation usually comes in. If you just want something close enough for a rough check what you can do is just "extend" the standard test cables already in place as at least the chracteristic impedance should be pretty much the same (50 to 52 ohms, typically). So, for example, if your antenna has a 16 foot coax lead then you can try "extending" the already compensated for test leads (assuming you have been using those and they were provided with the VNA) out to 16 feet with all other characteristics being the same. Not perfect but in the ballpark usually.
Though you could attach the DUT cables to the test cables and extend out to the full length of the combined cable lengths it should be better to attach the DUT cables directly to the VNA and just use the DUT. But this could depend on the mechanical stresses of the connectors and adapters used and you will have to make that call.
Speaking of adapters - try not to use them as much as possible, of course, as they will affect the measurements though, if in good condition and decent quality shouldn't by much especially when already doing a "rough and ready" approximation as the not fully compensated Port Extensions are anyway. But still - try to keep their use down and instead use only the minimum number of adapters possible. Better to actually get test cables that have the desired DUT connector at one end and the correct VNA connector at the other. Then you will have to have appropriate calibration standards that terminate in the same connection as the DUT so as to calibrate correctly. An alternative slightly less accurate variation is to have a set of the exact same leads terminated in the same connectors your standards use but otherwise exactly the same (length plus characteristics) as the cables you will use for connecting to the DUT. Second best option is to use only 1 adapter conversion so that you only do one connector type conversion - you really don't want to have to add multiple adapters for BOTH mechanical AND electrical reasons!
For the kind of test you are trying to do with a mobile antenna with fixed leads try and put the antenna on a flat ground plane with a cross section at least to a length needed for the lowest frequency you intend to test at (at the bottom of the civil air band it's about 25 to 30 inches; low band would be much bigger and you may have to omit that test or accept the otherwise present measurement compromise if including that band in your tests and using a groundplane size that is smaller than needed) and keep the antenna away from any metallic material as possible - say on a wooden table in the middle of the yard but with a metal sheet under the antenna for the ground plane unless the table is metal itself and can function AS the ground plane. Another option might be a car roof with the car located out in the open away from any metal (aside from the car body) objects.
Something I might do if given the same conditions is to note what the type of coax is that is attached to the antenna-DUT. Usually that is basic RG-58A/U or some equivalent for basic hobbiest mobile antennas. Then I would get an equivalent length of the same type, or as close as possible, and then connect the calibration standards to the end of that coax with the VNA at the other end and then run the calibration, open, short, and load for the test frequency range. Don't coil up the calibration test cable OR the cable to the antenna-DUT but try and run them both out as straight as possible away from the VNA. While at 50 feet this isn't really practical for most of us it should be doable if you have access to some reasonable open space at only 16 feet. Then you can avoid the Port Extension work-around.
-Mike