How can I make a dialog shop using leaderboard money?

Alright, so you're on the right track, with some minor modifications you will be able to achieve what you want!

DialogChoiceStarted returns two parameters, that you have already set variables for in your function:

dialog.DialogChoiceSelected:connect(function(plr, choice) -- plr here returns the player object of the player that clicked the dialog choice
end)

Thus, we will be able to use the variable "plr" to check if the player has sufficient funds

So after the modifications, the script should look something like this:

local dialog = script.Parent.Parent
local choice1 = "KatanaChoice"
local choice2 = "RocketChoice"
local choice3 = "SpinnerChoice"
local choice4 = "PistolChoice"

function deductMoney(stat, amount)
	stat.Value = stat.Value + amount
end

dialog.DialogChoiceSelected:connect(function(plr, choice)
	local stats = plr:findFirstChild("leaderstats")
	local bank = stats:findFirstChild("Bank")
	local cash = stats:findFirstChild("Cash")
    if choice.Name == choice1 then
		local price = 25000 -- set the price value to the price the item of the choice is
        if cash.Value >= price then 
			deductMoney(cash, -price) 	-- take away the money from the cash stat
			local katana = game.Lighting.Katana:Clone()
       		katana.Parent = plr.Backpack
		elseif bank.Value >= price then -- else if there is not enough money in cash stat
			deductMoney(bank, -price)   -- take away the money from bank stat
       		local katana = game.Lighting.Katana:Clone()
       		katana.Parent = plr.Backpack
		else
			print("Not Enough Funds")
		end
    elseif choice.Name == choice2 then
    	local price = 100000
     	if cash.Value >= price then 
			deductMoney(cash, -price) 
			local Rocket = game.Lighting.RocketLauncher:Clone()
           	Rocket.Parent = plr.Backpack
		elseif bank.Value >= price then 
			deductMoney(bank, -price)   
       		local Rocket = game.Lighting.RocketLauncher:Clone()
           	Rocket.Parent = plr.Backpack
		else
			print("Not Enough Funds")
		end
    elseif choice.Name == choice3 then
     	local price = 500000
       	if cash.Value >= price then 
			deductMoney(cash, -price) 	
			local Spinner = game.Lighting.AutisticShuriken:Clone()
       		Spinner.Parent = plr.Backpack
		elseif bank.Value >= price then
			deductMoney(bank, -price) 
			local Spinner = game.Lighting.AutisticShuriken:Clone()
       		Spinner.Parent = plr.Backpack
		else
			print("Not Enough Funds")
		end
	elseif choice.Name == choice4 then
  		local price = 8000
       	if cash.Value >= price then 
			deductMoney(cash, -price)
			local Pistol = game.Lighting.GLOCK18:Clone()
           	Pistol.Parent = plr.Backpack 	
		elseif bank.Value >= price then
			deductMoney(bank, -price) 
          	local Pistol = game.Lighting.GLOCK18:Clone()
           	Pistol.Parent = plr.Backpack
		else 
			print("Not Enough Funds")
		end
	end
end)

Note: Storing objects in lighting is not the most efficient way of doing so, you can use ReplicatedStorage (if it has to be accessed by local scripts) or ServerStorage (can only be accessed by server scripts). I left it the same you way had it though, set to lighting.

Strong suggestion: when asking questions on here, please ensure correct tabbing of the code, it makes reading the code much easier.

Hope this helped!