I went through this question on this board last fall but couldn't find it with the searchless engine. Here is what I can remember and it was all proven very true from my experience so far.
If at all possible, go with a starter set from Roland. The Yamaha's (it's only 'popular' competitor) does not have nearly as good a record for durability according to my research.
Make sure that at least the Snare is a mesh pad instead of rubber. You will instantly feel the difference when you try them oput in a music store. The snare is the drum (symbols aside) that you hit the most and your wrists will thank you for it. Also, you will want the mesh feel to learn how to do drum rolls properly. They are also adjustable so you can tune the feel and bouce the way you want it.
Hitting the rubber pads for Toms is good enough for learning but make sure you buy a kit that allows for converting them to mesh down the road in case you decide you like it and get serious. I'm keeping the rubber toms for a while yet but I already know I will want to change them out to mesh down the road someday.
Make sure the symbols and at least the snare have multiple sensors, "dual trigger." In other words, it at least knows the difference between a hit in the middle and a rim shot. My symbols change the tone as you get closer to the inside bell (just like real ones) and rimshots sound like rimshots. Some cheap sets don't let you do this.
I also bought electronic drums to use earphones and save my wife from the noise. Be aware the tapping is still a bit loud but nothing like the crashing and thud of an acoustic set. As long as she is in a different room with the door closed, I'm good.
You will want to get good earphones. Buds are useless and even cheaper open ear phones make them sound weird. Especially the kick drum. Fine for practice but you will want to start saving for a good set of cans down the road.
Finally, One of the other great things about electronic drums is that you can input tunes from your PC into the drum brain and listen to them while you play and still not bother anyone. Very quickly you will find that you want your laptop or monitor in direct view with a mouse within arms reach. This also is great for online drum tutorials as you need to hit pause quiet often.
I plan on making a little table beside me for the mouse but for now, I'm using a beer holder that attaches to the drum frame as a mouse holder the the floor tom as a mouse pad. And in case your wondering, the extra sticks get tossed and my stick holder becomes the beer holder. I wouldn't want Tom getting mad at me there.
If you are interested, I bought this set and I am very happy. Looks like they changed the 5 to a k in the model number and changed, probably upgraded, the drum brain but it's otherwise essentially the same. Roland TD-9K Drums
Another learning. Depending on your floor, you may find that the floor pedals start to slip away from you, especially the kick drum pad. The bases come with adjustable metal spikes for carpet and Velcro like pads for carpet but if you have hardwood or another type of hard floor, you will save a lot of frustration by buying a drum mat. I just bought a length of bulk, black floor mat material and it works great for cheap.