Soggy (hopefully not a reference to your new suit!) you won't need much under your suit if it's a 7mm (just looked at the bare site, and it doesn't seem to specify the material thickness...)
It's rare for temps at the bottom to be less that 4° or 5°C. (40° - 42°F). On rare occasions it will dip to 39F or so, but likely you will only be in this for a few minutes. Two days after the ice went out this spring, we had 33°F top to bottom and that was unpleasant.
So if you're suit is 7mm, I suspect that you would be fine in some kind if wicking undies... Typical of what you would wear as a base layer skiing. If you are inclined to be chilly, add a fleece layer. If the suit is 5mm or less, then you'll want perhaps a 200 weight layer as well. In either case, make sure it lets moisture pass. I wear a rubber Viking and was suiting up in hot temps on the weekend, then dove to about 170'. It was amazing how damp the inside of my suit was, just from condensation.
That fancy outfit from our friends at Pinnacle might be just the ticket, it not a tad fancy!