The K value of the bulb does not define light output (that's Wattage), but the colour temperature (K meaning Kelvin) the higher the K, the more "Blue" the light appears; the very high K values look somewhat purple/violet! As the light goes further into the purple, you will actually start to lose visable light output, so stick to the lower K values (6000K).
As to the (ill)legality of aftermarket HIDs: I ran HIDs on my old S2 Coupe for years - that had very old-fashioned reflector lenses and got it through every MOT with no issue. MOT testers are looking only for aim and equal brightness.
The main issues with HIDs is dazzling on-coming traffic, which is why factory fits have to have auto-levelling and headlamp washers as standard. If you retro-fit, ellipsoid lenses are a better start, and if you have headlamp washers even better. The most important thing I found was to make sure the aim is spot on, be sensible and keep it a few degrees lower than required and ensure it's not beaming across to the right. Keep the lamps clean, don't go for a very high Kelvin lamp and you'll be ok.
As mentioned above, one of the best mods I think you can do because you can actually see where you're going in the dark, which is a distinct bonus!