So the weather has been warming up lately...which means car cleaning time!

After a quick wash at the Coin Op car wash (not warm enough for hand washing yet...), we noticed many swirls in the TSX's paint (black, 2004), especially on the hood. We bought the car back in December, so we haven't touched it with any type of cloth yet.
However, we believe its caused by the snow brush we use to clear off the snow (the car is parked outside).
We will give the car a hand wash and WAX, but are there any more steps we should take to make the paint look like new? We use microfibre cloths from Costco to apply wax and to wash the car. I was thinking of Meguiar's 3 step system; Cleaning Wax, Polish then Wax.
Black is such a PITA to take care of.

But looks great when clean.
Any tips are welcome.