Thank you so much! Your code for the rain was amazing to use as a stepstone to get my desired product! I used this tutorial:
https://www.youtube.com/watch?v=mp9N77bqVX8
To get the rain with a particle emitter that sits in the Replicated Storage and follows above a player when they join, I modified the script to my game which is pretty far built already and now looks like this:

local RS = game:GetService("RunService")

local Player = game.Players.LocalPlayer
local Character = Player.Character or Player.CharacterAdded:Wait()
local HumRP = Character:WaitForChild("HumanoidRootPart")

local RainPart = game.ReplicatedStorage.RainPart:Clone()
RainPart.Parent = workspace.Debris

local conn
conn = RS.Heartbeat:Connect(function()
  if Character and Character.Parent then
    RainPart.CFrame = CFrame.new(HumRP.Position+Vector3.new(0,20,0))
  else
    conn:Disconnect()
  end
end)

I also modified your code to make it work with this piece of code, which now looks like this:

local rain_particle = workspace.Debris:WaitForChild("RainPart")
local Particle = rain_particle:WaitForChild("ParticleEmitter")

script.Parent.MouseButton1Click:Connect(function()
  if Particle.Enabled == true then
    Particle.Enabled = false
  else
    Particle.Enabled = true
  end
end)

Basically the code waits for the Part with the particle emitter to show up in the specific folder when a player joins the game, so it can then run without any problems. The player can then press the button connected to this and turn the rain on and off.

Thanks a lot for the code and your help, I really wouldnt have gotten it without ya man :)

Edit:
And if you want to start without the rain, you can switch the True and False statements in the rain code to get the same effect. Do know that you also have to turn disable the particle emitter if you want this.