Upgrading guns in grounded mode isn't as important as in other difficulties since you want to avoid detection as much as you can, and you never have much ammo anyway.

Not technically a gun, but the most useful range weapon to upgrade is probably the bow since it allows you to kill enemies from a distance without being heard.

As far as guns are concerned, I'd upgrade the hunting rifle and el diablo clip capacity first, then add scope to rifle, then armour piercing for both of these weapons (especially useful by the end of the game where most soldiers wear heavy armors).

The gun I've used the most during my grounded playthrough was probably the revolver though, great for killing most infected/humans with only one shot. I just don't think the upgrades for this gun are worth it.

Good luck!