I was glad to wear the hospital gowns and use the disposable undies. It truly is a mess, giving birth and the afterbirth bleeding. It would have ruined any of my clothes. My opinion is why would I want to wear my own clothes only to get them completely bloody? Why would I want to have to clean them? After childbirth, the easier you can make things, the better. Just wear what the hospital gives you and let them worry about cleanup. You won't really care about what you are wearing afterward anyway. You will more concerned about the baby and your well being. And, hospital gowns are easy to replace while you are in the hospital. If they get soiled, just ask the nurses for another one.
But, I would bring some extra pads, not the menstrual ones and definitely not cloth. Get some of the large, bladder control pads from the drug store. They are the only thing close to what the hospital will give you and you will need something large. The hospital pads I got immediately after child birth were huge, bigger than any menstrual pad. For at least a couple of days, you will need some HUGE pads. After that, regular large menstrual pads will be fine and I imagine that cloth will suffice as well as disposable.
Regular bikini underwear, which I prefer, won't do either. I had bought waist high cotton undies just in case and I was glad I did. I wore the large undies with super sized menstrual pads for a few weeks while I wore pads, healing. You should also buy some latex or equivalent gloves. They are great for filling with crushed ice to put between your legs. You can throw them out or wash them when you are done. Also, an inflatable cushion, available at a drug store or the hospital may give you one, is a god send.