The CPU does ship with a cooler which will work fine. Generally keeping the CPU cooler allows it to boost for longer and theoretically last longer, so a better cooler is a good idea, but it isn't a must, the stock one will work fine.
If you can stretch for a 3080 then definitely go that route. It's a lot quicker.
Also, AMD GPUs are about to become available (for about 3 minutes before they're sold out, much like nVidia's ones), so it may be worth waiting for those. Tomorrow at 4:00PM the embargo lifts and we will see benchmarks and so on which will give us an idea about their relative performance and price/performance vs nVidia, so it might be worth waiting for that.
As a note, I have a Palit 1070 and it's been totally fine, though I think the Gigabyte will likely be a better part overall.
I chose that one only because I have it and I love it. It's also one of the best in terms of thermals, before you start getting into big-money territory.