Sounds like most of your lathe work will be done with a tool post grinder. I don't think the power of the machine will be a deciding factor, since the grinder will be doing the work.
For milling operations, you will need to ensure that the machine is capable of sufficient rotational speed for the size of the grinding wheel or stone. Depending on the wheel size, that might mean 3,000 - 5,000 rpm.
While accuracy of your part may not be critical, accuracy of the machine still is. Very light passes are required -- each increment should be less than the protrusion of the diamond bits from the wheel surface. IIRC, depth of cut for an 80 grit diamond wheel would be less than 0.003" and for a 320 grit wheel about a tenth of that -- 0.0003". You can control the 3-in-1's depth at the first example, but probably not to the degree required by the second order of magnitude, so forget really finely finished surfaces.
I don't know of any common 3-in-1 that comes with a coolant system from the factory, however after-market and shop fabricated examples abound. One of the simplest flood-coolant systems in use is simply a shop-modified parts cleaner -- they come with the pump, reservoir and gooseneck nozzle. The home machinist just has to modify things slightly with some piping so the chip pan drains back into the reservoir and the nozzle is mounted in a suitable location. You would want to consider some splash shields, because at those rotational speeds, things are going to get messy.