Clay bar will remove fall out and contaminants that stick to your paint. It will not reduce swirls at all. Actually, it will create more swirls if you are not careful with it.
Polish is the only way to rid of swirls. Menzerna PO106FA or PO85RD are good polish for minimal swirls. I know Menzerna has a new naming system now, but you could still figure out what they are. There are other cheaper options out there too. I would recommend a green or blue detailersdomain uber pad for your orbital.
If you don't want to polish, a cleanser like Prima Amigo is good for "covering up" swirls and ridding of oxidation. It's a dark liquid cleanser so it will work great on your black car.
Then seal everything up with your favorite wax and or sealant. Collinite 845 is mine but everyone will have different opinions.
There are plenty of other products out there, but I just mentioned the ones I own and use.