For an 8 or 9th gen processor, you will need a lga1151 300 series motherboard.
If you do not want to overclock, any will do.
However, if you have a K suffix processor, I would highly advise spending a bit more for an overclockable Z370 or preferably Z390 motherboard.
You need not overclock initially, but that is what the Z processors are designed to do.
It is as simple as raising the default multiplier.
You are leaving some 20% performance on the table.
Your budget will give you many options.
Here is one
https://www.amazon.co.uk/ASRock-90-...+motherboard&qid=1553444917&s=gateway&sr=8-10
If you will buy a K processor, I highly suggest the i5-9600K
The price will be similar but the 9600K runs cooler because it has improved soldered heat spreader.
If you will be using a discrete graphics card, the i5-9600KF should show up soon.
It is the same processor without integrated graphics.
I do not know if the price will be anything less as you might think.