I struggled with how to mount the cabinet door on mine as well. I'm sure I made it harder than it needed to be, but I have no skills when it comes to woodworking. So keep this all in mind when reading below.
I ended up getting European style hinges like these:
http://www.woodcraft.com/family.aspx?FamilyID=1060, but from Home Depot. The hinges I got were on the door hardware aisle in some bins across from the door locks.
I also was worried about the weight of the door and it pulling the screws out since the screws that hold the hinge on are pretty small. I ended up cutting the door into two halves, which actually works just fine. There's a gap on the front between the doors (maybe 1/2"), but its not a big deal to me.
As for mounting, I spent a bunch of time trying to get the hinges mounted right, and ended up having to add a couple of pieces of MDF to the sides of the cabinet like you have to get it all sized right so the doors didnt rub (the first piece wasnt wide enough, so I had to add a second smaller piece). If you go with those type of hinges, you'd actually probably need to extend the sides a bit from what you have so you can open the doors properly.
Here's a couple of pictures that I took that may give you some more info. The first is what my doors look like from the outside. You'll notice a small gap in the middle between the doors, as well as on the outside around the doors. If you plan to set the doors inside the cabinet like this, I'm not sure there's a way to avoid the outside gap (but I'm also not very handy).

This is what the doors look like when opened. The MDF coming from the side is nearly 2 inches. As I said above, I had to add another strip to the piece since the first one wasnt cut wide enough.

Hope this helps. If you have more questions, just ask.