What is the best way to share a table(that can be changed) between different scripts?

What the best thing to do would be to store all your information in a Library (which is a type of table) inside of a Module Script on the Server Side. The Server is the best place to store this type of information because it's more secure from exploiters rather than keeping it completely visible and view-able on the client.

A Module Script takes the whatever side you put it on, Server or Client. ReplicatedFirst would be Client while ServerScriptService would be Server.

To access it from the client, you would want to use a RemoteFunction to Invoke the server and return the data you need.

Example...

Library

local data = {	sword = {damage = 5, cooldown = 1},
			bow = {damage  = 10, cooldown = 1.5}
		}

local module = {}
	module.getData(object)	-- Where object is a string
		return data[object]
	end
return module

LibraryConnector Script

local LibraryConnector = game.ReplicatedStorage.LibraryConnector
local Library = require(game.ServerScriptService.Library)

local function onDataRequested(player, object)
	return Library.getData(object)
end
 
LibraryConnector.OnServerInvoke = onDataRequested

Client Local Script

local LibraryConnector = game.ReplicatedStorage.LibraryConnector -- RemoteFunction

local swordData = LibraryConnector:InvokeServer("sword")

Helpful link for understanding... Remote Functions/Events