The 845 is 62€, the 860K is 73€ and the 880K is 83€ and the i3-6100 is 30 bucks more. 30 bucks I would have to pay from the GPU budget. This is a budget build and I'm fully aware of the constraints. My main rig actually has the i3 so no need to convince me it's better. The question is: Is spending 20€ more on the 880K over the 845 justified on a budget build or is the performance difference too minuscule? Keep in mind that if this pc is upgraded it'll be another budget gpu in two years or so anyways. So I'm wondering if the 880K might be less of a bottleneck in the future as both CPUs are gonna be pushed to their limits.
I know one has to set a budget, but it seems like false economy to save 30 dollars on a system that will be used for years. I mean 30.00 is less than the price of one meal eating out with your significant other. It is also what, maybe 5% or less of the cost of the entire system. The i3 is also more efficient, especially compared to the 8800k, even more so if you overclock the 8800k, so you will save a few dollars a year in energy costs. It would also have an upgrade path in 2 or 3 years when you could upgrade *both* the cpu and gpu.
Baring that, I would suggest waiting for AM4, so in a few years you could upgrade both cpu and gpu as well. Problem is, if you absolutely cant or wont pay an additional 30.00, I am not sure what the price of Bristol Ridge and AM4 motherboards are going to be.
I do think the 8800k would be adequate for now with an RX460, but if you plan to keep the system several years, and upgrade the gpu in 3 years, I definitely would get a system for which you could upgrade the cpu as well.