Alright, when you are meditating its best to be in the most comfortable position. Laying down isn't the most ideal because it's easy to fall asleep. However laying down, your letting your body relax like you are in a trance. So, take into mind that you need to reanimate your body before standing up quickly afterwards. You can become dizzy like you did and I have even heard of some passing out from not reanimating their body and just standing up.
A simple visualization that you can try is draw a circle, then draw dot in the center that takes up 1/4 of the circle. Stare at the image for about 2 minutes then close your eyes and focus on seeing the image. Keep doing that until you can visualize that without having to see the circles. Then you can move to more complex things.