Most people on here go for the 2.2 kW model as it will cut all those materials and you can fit a range of cutters. 4kW sounds too much as it will be heavy and you are paying a lot for it. 2.2 can be bought for around £200 or so including VFD delivered.
But you might have other things in mind or be looking at high volumes or something. You can probably run at lower speeds as you'll have more torque. I think Sylavski has a 3kW spindle so he may have a view on that kind of power. Wait for a second opinion before deciding but it seems a bit high for what you need.

Noticed there is a spindle for sale on here which has an ER16 which is useful. Make them an offer ?. . .