The red tape on the wire could be meaningless or it could mean that it is the hot wire. I’m assuming you don’t have a voltage meter or a voltage detector to test with?
If you do have a voltage detector (you can get them at lowes and home depot also) turn the switch off and see which wire is hot. If the white, likely no good. If black, likely good.
You can’t ever really know until you test them…
You want your scenario to be like the image on the left.
http://www.diychatroom.com/attachments/f18/80570d1391162914-switch-leg-correct-switch-loop3.jpg
Others will say it, so I will. If you need more help you should probably call an electrician.