Regarding usage of Task.Start() , Task.Run() and Task.Factory.StartNew()

Short answer:

If you are not using nested children's tasks and always want your tasks to be executed on Thread Pool it is better to use Task.Run.

Long answer:

Task.Run and Task.Factory.StartNew both provides support for creating and scheduling Task objects so we don't need to create a Task and call Start()

Task.Run(action);

Is equivalent to:

Task.Factory.StartNew(action, CancellationToken.None, TaskCreationOptions.DenyChildAttach, TaskScheduler.Default);

And

Task.Factory.StartNew(action);

Is equivalent to:

Task.Factory.StartNew(action, CancellationToken.None, TaskCreationOptions.None, TaskScheduler.Current);

Task.Run uses TaskCreationOptions.DenyChildAttach which means that children's tasks can not be attached to the parent and it uses TaskScheduler.Default which means that the one that runs tasks on Thread Pool will always be used to run tasks.

Task.Factory.StartNew uses TaskScheduler.Current which means scheduler of the current thread, it might be TaskScheduler.Default but not always.

Task.Run is a shorthand for Task.Factory.StartNew with specific safe arguments:

Task.Factory.StartNew(
    action, 
    CancellationToken.None, 
    TaskCreationOptions.DenyChildAttach, 
    TaskScheduler.Default);

It was added in .Net 4.5 to help with the increasingly frequent usage of async and offloading work to the ThreadPool.

Task.Factory.StartNew (added with TPL in .Net 4.0) is much more robust. You should only use it if Task.Run isn't enough, for example when you want to use TaskCreationOptions.LongRunning (though it's unnecessary when the delegate is async. More on that on my blog: LongRunning Is Useless For Task.Run With async-await). More on Task.Factory.StartNew in Task.Run vs Task.Factory.StartNew

Don't ever create a Task and call Start() unless you find an extremely good reason to do so. It should only be used if you have some part that needs to create tasks but not schedule them and another part that schedules without creating. That's almost never an appropriate solution and could be dangerous. More in "Task.Factory.StartNew" vs "new Task(...).Start"

In conclusion, mostly use Task.Run, use Task.Factory.StartNew if you must and never use Start.