Once you're in the Act 2 Missions, other weapons may take priority, but it's still good to have your pistol as backup. Due to the inexpensive cost of your upgrades, it's very feasible to buy all the way to Pistol 3 before getting out Act 1 Missions.
Your pistol is your first basic weapon, and is strong enough to get through many of the early missions. These upgrades increase your ammo capacity of all grenades, including frags, flashbangs, and even Farts in Jars.