How to prevent Bullet Spam?

Well, after reading your script quickly I noticed a few errors that'd cause your problems.

First, I'm gonna cover your problem in the comments, where you said it's able to fire when your ammo is at 0. That's because of line 3, where you used Ammo.Value >= 0. Instead, it should be either Ammo.Value > 0. or Ammo.Value >= 1. Now, as for the second part, the fix should be kinda simple. Try moving the wait(FireRate/60) to line 17, then add GunReady = true below it, kinda like this:

Mouse.Button1Down:connect(function(Mouse)
Firing = true
    if Active == true and Ammo.Value >= 0 and GunReady == true then
        GunReady = false
        Dead()
        CreateBullet()
    end

    if Active == true and Ammo.Value <= 0 then
        Firing = false
        Empty:Play()
    end
    GunReady = true
    wait(1)
end)
wait(FireRate/60)
GunReady = true

Mouse.Button1Up:connect(function(Mouse)
    Firing = false
end)

If it doesn't work, let me know, as there are a few things I'm not sure of.

First off, line 1 has 2 errors: connect is deprecated, switch to Connect. 2nd error is you passed a parameter of "mouse" when the Button1Down event has no parameters, PLUS you already HAVE the mouse defined. And yeah the ammo stuff was already answered.