I leave my piercings in pretty much all the time. The faster-healing areas can close around a piercing pretty quickly, and I don't want to take the chance. I'm not sure how fast bellybutton heals, but I'll bet a clit piercing would be hard to get back in if you had it out for more than a 6-8 period. Whether the hole from the bellybutton would show I suppose would depend on the size of the piercing, but I don't really know a lot about the bellybutton. I wouldn't think it'd be very noticeable unless you were really close, or looking for it.
Nipple rings can be taken out and usually don't affect breast feeding, but it is a possibility. I don't know what a clit piercing would do during birth... I'd assume you'd want to take it out for that.
My nipple is more sensitive than it used to be before I pierced it, so that's a big thumbs up
and oh the stories I've heard about clit piercings.
Go check out
www.bmezine.com and read up on the piercings you're considering. People submit their personal experiences for you to learn from, and there is a risks section that explains a lot of the potential dangers of piercings, mostly from neglected aftercare.