Engelberg is easy to access by train; a day trip from Zurich is easy. It also has a long season and reliable snow, partly due to the glacier and that the slopes are north facing and/or otherwise in the shade for much of the day (but therefore can be cold). Lift infrastructure is more modern than Andermatt.

Yes, there are a lot of Asian tourists, although I've seen this many other places in Switzerland (including Zermatt); summer and winter. There was a new cable car in winter 2015/16, now 16 mins and direct to Stand without a change half way (so bear in mind when reading old reviews). Many tourists still take the old train. So if you're on the lifts around 9am at the weekend, it's really ok and no worse than other big resorts across the Alps, in my view.

Queues can be big to buy the ski passes, so recommend you get these online before you go: load them onto your Swiss Pass o keep an old Engelberg lift pass for this. Otherwise, there are some automatic machines outside, but you can't get your Snow n Rail discount this way.

Once on the mountain, the main ski area has reasonably long slopes, and nearly all red/black in the main ski area. The area is split into two parts, connected by a horizontal chair lift, which is a bit annoying, and getting to/from this lift is not easy for a beginner. If you're a beginner, Engelberg is not a great resort. The purported blue run in the main ski area (right hand side of the map) is actually quite tricky, undulating from steep to flat (only a blue on average really), and frequently off-camber. The runs on the glacier are probably a better bet, being wide and consistent gradients, even if some red. There is, however, a very tame area of drag lifts on a lower part of the mountain (access by the mountain train), and a smaller ski area across the other side of town. I've never tried these, but they looked quiet.