It all depends how high the cross is, how far off the ground you are. If you arrange your cross so that your unbound feet would touch the ground, then you should be perfectly safe for height, but you may feel you are missing something.
Personally I find the sensation of being off the ground is the important thing, however high or low you are, it is that sense of no longer being directly connected to the ground.
As for wood, a 90 by 90 upright is plenty strong enough, and a 90 by 70 or even 90 by 45 cross bar should be enough for an average sized person. It depends on the wood, and how you fix the parts together. For effect, you may want pieces broader than 90cm, it will look more impressive.
Make sure your cross or frame is sturdy and well fixed so that it doesn't move around (or fall down!). You may want to use existing architectural features, such as veranda posts or internal supports. Work with what you have