Hanging Bracket suggestion

Yes you can connect them with one cable. The bulbs only run about 12 watts each so three of them dosen't even account for the power draw of one 60 watt incandescent bulb. If you know nothing of electrics you may want to ask someone who does to to the physical wiring connections for you, it's not difficult so you shouldn't have to go to an electrician.
That light bracket should work well. The only thing I notice about it is that it appears to have metal bolts to tighten the side brackets on to the glass of the aquarium. If that is true then it's probably a good idea to either replace them with nylon bolts (available at RC hobby stores) or put something softer underneath them to prevent them from actually tightening directly onto the glass. A piece of soft plastic would work well.

Like mentioned above, lights doesn't sound enough lights. Before you invest in a bracket make sure you can use it if you need to change fixture or different lightings. My tank is against the wall, I used a wall bracket to hang my lights and it doesn't put any weight or pressure on the tank itself. I hang the bracket little higher and I use adjustable cable to adjust the lights. For me, it's very important that I can adjust the lights higher or lower, that way you can adjust it depends n your plants need.