Virtually no monitor displays accurate color without calibrating and profiling. A device called a Colorimeter is a cost-effective tool for this. XRite makes several, including the ColorMunki and i1 DisplayPro:
i1Display Pro Monitor Calibration Device | X-Rite
The colorimeter will help you to be able to trust the color that is coming off the monitor. It does nothing to effect the printer. For that, the place to start would be the HP Media Solutions Locator - here is a link:
PrintOS – Media Locator
There are literally hundreds of media presets for the Latex 300 Series printers. Pull down the preset (OMS file) for the media product that you are running. You can search by brand, application, sub-type, etc. Once you have the file, install it to the printer via the Embedded Web Server browser interface.The other way to do this is directly from the printer's front panel.
Once the media is resident on the printer's hard drive, physically load the media, and when the printer is in ready state, run a Color Calibration for the loaded media: Settings Icon > Image Quality Maintenance > Color Calibration > Calibrate. This procedure takes about 12 minutes. Once it is complete, you will have done what is needed to get great color from your Latex 310 printer.