On a new car it is still certainly worth claying because although it's new generally the paintwork will not be as smooth as it should be. Go for a fine poly clay rather than anything too aggressive and use plenty of lube, a must on black.
Once clayed it gives you a uber smooth surface to work with and you will find that this helps for the following products to bond and be much more durable.
As for using a DA - this is one of the easiest machines to use and unless you have no common sense cannot cause any major damage (particularly on VAG paintwork which is hard). For example are you really going to stand in one place on the panel for 5 minutes on the highest speed setting?! No I don't think so. You can achieve a much better shine and depth from using one, however....
If your using new products then I would suggest trying by hand first to accomplish a good result and once you feel more confident proceed from there.
Our Juicy detailing Beginners Clay Kit contains a 75g fine yellow poly clay bar; 500ml Juicy Lube and a EuroW All Purpose microfibre all for £9.99 which has to be the cheapest kit in the market place.
Juicy Detailing Beginners Clay Kit | Detailing Clay | Juicy Detailing
It is important to perfect the wash and dry technique to preserve the paintwork. Also invest in a decent quick detailer such as Chemical Guys Clear Seal or Chemical Guys Hybrid V7 which not only bring back that shine and depth but removes water marks too which are a PITA on black.