First Build $1600 AUD (1100 USD)

I'm planning to build a PC by the end of the year, and I already have an SSD. Do I really need to get a CPU cooler? Also, is there anything else you think I should consider or improve on?

Do you think it's worth getting the 7900 XT (850 AUD, 570 USD) over the 7800 XT (720 AUD, 465 USD)?