PC for Sim Racing

I don't actually have much experience with sim racing set-ups, but I know a little about what a powerful system looks like on a tight budget. You don't say what monitor resolution you're powering, but the GPU will have to be strong to run multiple monitors at high framerates. To do that within your budget, I think your best bang-for-buck ATM is a the Lynx 4 pre-built.

https://www.digitalstorm.com/configurator.asp?id=4543278

The 12600K is a very powerful gaming CPU. That's paired with the RTX 3070 Ti for the most powerful set-up you can get here anywhere near that money. The drawbacks are that, because of that price point, it's light on storage, and you might want to add another 16GB of RAM at some point. Those are easy upgrades. You could have them done for you at a computer shop and still be well under your budget

A custom build within your budget would use it all up, and not be worth the extra spending IMHO. Here's a sample:

https://www.digitalstorm.com/configurator.asp?id=4543282

The CPU is rated ~11% better, the primary drive is as fast as you could need, and there's 32GB of RAM. The motherboard is upgraded. but it's $725 more.

If you want to go the custom route, your very best bet is to wait for the RTX 4070 to come to market. Rumor has it, Jan 5. It is slated to be about 40% better/faster than a 3070 Ti, and will be around the same price point. It will also kick the 3080 Ti to the curb. The 4080 comes out tomorrow. Perhaps DS will have inventory to offer it. It will be over budget.

Choices, choices.