Make sure your breaker takes that type of breaker (Siemens Q style). But as for rating it looks right. There are numerous types of breakers. I took some close up pictures of my breaker panel information sheet, and the breakers themselves and then went down to Lowes. I picked up a NEMA 14-50 receptacle, a breaker, a face plate and junction box all for about $20. I whipped out my phone and matched the breaker information on my pictures to the correct breaker at Lowes.
You only need a 2 pole breaker, you only need to break the hot feeds. Your neutral and ground go back to your bus bars in your main panel.
As for wire I got some free THNN wire from work, and some scrap conduit. So I had 4 sepearte wires. Your wire is Romex 6-3 with ground. It actually has 4 wires in it. You have 3 wires at 6 gauge which are for you two hots and neutral. There will be another ground wire which will be smaller. Your neutral and ground skip the breaker in your panel and tie directly into the neutral and ground bus.
Thanks to all that replied, I think I now have enough info to put together my home charging solution