I don't have too much experience myself, but I did buy a danskin suit (the only one I could try on, I was so afraid to buy without trying -- and I would have been way off on sizing). I am also a C/D myself. The shelf bra feels like it might support me for a short run and definitely for walking, but is questionable for a longer run. I wear my normal sports bra underneath it (the Hind Nexus) and it feels a little tighter than just the suit alone around the shoulders/armpits. I have been running in the suit with sports bra since I got it.

If you have anywhere you can try (no pun intended!) a tri suit on, I would take your sports bra and give it a shot. You might be able to get away with the shelf bra, you might feel okay with both, you might feel better in a tri suit without a shelf bra and just use your sports bra, you might feel better in separates.. it's hard to tell. You might have to go a size up from the normal size to fit with a bra, provided that fits everywhere else too (that didn't work for me, it was way too loose up top and around the legs).

I really like the feel of the suit over separates, but I am glad as the first time buying the suit that I had a chance to try it on first. The first thing I did when I brought it home was try it with and without my sports bra. It's definitely gray area, but if you are used to wearing good support and want to run, you'll probably want to wear the bra under the suit. There are some suits (TE sells many) that don't have the shelf at all.

Danskin says their suits are good up to a C, I think that's fairly accurate unless you're a "generous" C (or sometimes/always a D). I'd imagine most suits are made from similar material. You could always bug their customer support to find out