Note that there are no upgrades for protecting your cars. If you have only that upgrade, grenades and such may still hurt you, but even STAG's laser weapons won't make a dent in your health.
The most game-changing upgrade is arguably Damage - Bullet 4, which makes you invincible to enemy bullets.
Damage Upgrades, can make a huge difference in gameplay, as they reduce how hard you're hit by enemy fire. You might be able to get away without them on Casual difficulty, but it's almost necessary for Normal difficulty, and it's definitely necessary for Hardcore difficulty. The game is setup so that buying upgrades is practically required. For example, you may reach the point where you never fire your pistol, so buying any of the Ammo - Pistol Combat Upgrades would just be a waste of your resources. You should buy the upgrades that interest you or are the most helpful. Some of the later upgrades are incredibly expensive, and it's doubtful you'll be able to afford everything by the time you're done with the story unless you do a lot of waiting around or play Activities over and over. Upgrades have nothing to do with Achievements or Trophies, so don't feel pressured into buying everything.
