It doesn't mention the length, but I need it to be at least 3 inches long. Would this one work?
For god sake don't buy a drill bit online! bring the screw (and wall plug if needed) down to your local hardware shop and size the drill bit in person. Drill bits vary in length depending on the diameter of the bit. i.e. the wider the bit gets, the longer it is. small bits are very short because if they were any longer they'd snap when you try to drill with them. You need to consider two things when choosing a drill bit: 1. The length of the drill bit should be very slightly shorter than the screw. 2. The width of the drill bit should only be as wide as the solid shaft of the screw. Of course, the drill bit can be longer than the screw, you just have to remember how deep to drill into the wall!
dry wall, plasterboard, wall board, sheet rock, all names for the same thing. Any drill will work on wallboard, or just drive a nail through, that will make a fine hole. Why 3 inches, that is too long? Warning, there could be wires or plumbing inside the wall. That is why you should not drill in more than an inch. Wallboard is less than an inch. If you hit a stud (and that will be obvious) 1 inch into the 2x4 will be plenty for a screw and will hold anything. Also, some new construction uses steel studs, which need special screws. Again, it will be obvious if you hit one of these. .
That one will do the trick if it is three inches long. For all intents and purposes, plasterboard and dry wall are the same thing. Remember, however, if the think you are sticking in is a screw that is 3/16ths, you don't want to use a 3/16 drill, use one smaller so the threads have something to grab.