What power of spindle for cutting 4mm phenolic with 3mm cutter?

I have a 3 axis CNC router that I will mostly be using to cut 4mm thick paper/phenolic laminate. I will cut through the full thickness in one pass using a 3mm carbide helical cutter.

I want to get a Chinese water cooled 3 phase spindle.

Can anyone recommend what power of spindle I should use?

If that's all you want to do, I doubt that you need more than an 800W spindle. After all, you could probably take a cut like that with a 600W hand-held router. I think a lot of us have spindles that are significantly over-powered for what we ask them to do, but in my own case that is purely because the usual 2.2KW spindle will take an ER20 collet which allows 1/2" shank cutters; if you don't need bigger than ER11 then I'm sure that the smaller spindle would be fine. However, incremental cost in going up a size is not that great, so might be worth doing to give a margin.

Thank you, I think I will get am 800w. Low noise is also important. The only problem with the small collet it that I will need to face off the nylon block I am using for the bed. I guess I can use the original Porter Cable router to do that.

Not sure how the noise level varies between the different rating spindles, but certainly there's a lot to be said for water-cooled spindles from that point of view. I wear ear defenders when using a hand-held router and any other noisy power tools, but I can stand next to my 2.2KW W/C spindle running at full chat and still hold a conversation with someone next to me. The noise of the cut is greater than the noise of the spindle itself if you are removing any significant amount of material.

Couple of days ago I went from a 1/2" collet holding a 50mm facing cutter, used to flatten the spoil board, to a 0.4mm cutter in a 3mm collet for engraving some text. Versatile things, these spindles!

Nicholas the biggest consideration is weight. The 2.2Kw is by far the better option as it provides more options in cutters sizes. The down side is it's much heavier than 800w or 1.5kw.
If your Z axis can handle the weight I'd always go with 2.2Kw. There is no difference in noise between them only weight.