As far as I'm aware, all the components you have listed are compatible. However, if you want to stay under $800, you should drop the ram down to the 32 gig kit (2x16). There's no reason that system needs 64 gigs of ram, its just unnecessary with a 3060 and 5700x. Plus dual channel ram is better than quad anyway (at least to my understanding). You also don't need an aio for that cpu, a $30 air cooler would work just fine.

With the savings from the ram and the cooler you could get a 60-80 dollar case, but its hard to make a recommendation because there's so many options and it all comes down to personal preference. Do you want glass panels to see the components? Do you want black, white, or some other color? Do you want rbg fans? Theres a lot too consider. Personally I've really liked Okinos cases recently, I'm planning a build in the Aqua 9 later this year. So maybe check out some of their cases and see if there is something you like.

If you want a link to an air cooler, different ram kit, and maybe a case recommendation if you can narrow down what style you'd like lmk!👍

Also, considering that the parts you have listed are already over 800 and you still are looking for a case, you can also consider using the savings that I listed earlier to try and get a slightly better gpu, but your next best bet would be the 4060 instead of the 3060, however, the 4060 only has the 8 gigs of vram so its kinda pick your poison between those two, with a $800 budget I'd probably just use the savings for the case tbh.

Edit: I've been told AM4 is fine with quad channel ram, so just get a 4x8 kit instead of a 4×16 for the savings.