Your new HH has ALMOST everything you need for starting out.
You are correct that you will need some stakes for the tarp/side tie outs. If you're looking for something simple and cheap, you can get some aluminum gutter-spikes from your local hardware store.
Also, I would recommend some sort of spare cord (something small diameter) for tying out your tarp ridgeline. The stock HH method uses prussik-sliders on the ridgeline itself, but I think you'll find that you can get a much more taut pitch from it if you tie at least one end to the tree instead.
Good luck and congrats on your new hammock.