Is it possible to download a smaller GRIB GFS file with specific parameters only (e.g. surface wind and temperature values) rather than hundreds of MB of data? If so, what is the usual approach to achieve this?
Well, after a bit more of search and after forgetting how I even ended up on this page, there is one very helpful (official) filtering page right here on NOAA "website". Combining "levels" with "variables" (all acronyms are described here, also on official NOAA "NCEP Products Inventory" page) I managed to filter the data.
Selecting "Show the URL only for web programming" checkbox on the bottom of the "filtering" page shows up the URL needed to download specific file, e.g.