I would suggest that you select a few motherboards that are in your budget and then research the mobo manufacturer support page for which CPU can work at what BIOS level.
I was recently looking at an office build and it seems like I recall many of the 400 series mobo being able to use 11th gen with a BIOS update? Pricing on the 500 series chipsets/boards was seemingly really high.
Here is the lowest priced one I found on newegg for $65 https://www.newegg.com/p/N82E16813162011?&quicklink=true
Yes, it will also support 10th gen i3-10100F.
Considering the high price of current graphics cards, I would spend a bit more on the i3-10100.
The integrated HD630 graphics will run a 4k monitor via displayport at 60hz.