The rungs are often very rough and a good pair of padded gloves (for climbing or cycling) will be your best friends. You'll avoid hurting yourself on the cable which often has broken strands.
Additionally, in the event of a fall they'll be nice to you!
What type: leather cycling gloves (leather on the inside part of the hand) or gloves specially made for Via Ferratas. A bit more expensive, but they do a better job. Proper shoes, no tennis shoes!
What about the shoes?
Shoes with a vibram sole if possible.
You don't go to the mountains with mocassins or tennis shoes unless your name is Kilian Jornet. So for via ferratas, leave your tennis shoes in the car and get the proper equipment.
With tennis shoes the rungs hurt your feet and it's often slippery.
If you are going to be in contact with the rock a good vibram sole will help you out a lot.
The same goes for the way down. Proper shoes are essential (and sometimes ski poles are necessary for those who have knee problems)!