It's probably best to fly to most resorts from the UK. If you'll be in London you'll also be well positioned to take the train to a few of the resorts in France and Switzerland - this has the advantage that catching the sleeper in Paris can give you one or two days extra on the slopes.
Most flights to airports handy for the Alps are around one and a half hours, then anything from half an hour to three hours (or more) to transfer to the resort.
Also remember that most ski holidays in Europe are done by the week, not as weekend trips - this is borne out in the difficulty in getting accommodation for anything other than Sat-Sat or Sun-Sun. There are plenty of operators providing packages of flights, transfers and hotels. It is still also possible to DIY.
The snow will not be as good as American resorts, but you will be able to easily find larger areas with more variety in terrain than all but the very largest of American resorts.
The trails (get used to calling them pistes
) are marked as previously stated: Green, Blue, Red and Black (some resorts are adding yellow runs - sort of 'triple black diamonds' - marked off-piste runs). The levels don't directly correlate. NA greens are equivalent to Euro greens and most blues. NA blues range from the toughest Euro blues to reds. NA single blacks are tough reds and easy blacks in Euro-land. Meanwhile double black diamonds equate to the tougher blacks in Europe. Of course, as ever, this isn't a science, and throughout the world resorts will grade things differently, often just to make their piste-maps look more appealing to different level skiers.
Pow is less bounteous than North America, although when it comes it's as good as anywhere (was playing in it last week whilst in Wengen - although it was warming too much by the end of the week). And yes, you get some insane chutes (couloirs) and some horrifically vertical drops (often covered in car sized moguls - take a look at the 'Wall' above Avoriaz dropping into Les Crosets).