I'm a male level 7 skier, but as a developing intermediate what I needed most was: good edge grip for that hard pack (learned to ski in Western NY state), and relatively damp skis, because too much chatter makes you feel like your platform is not solid and like you are not in control. To me here's nothing more unnerving than tyring to learn to do more aggressive carves and having the skis start to skid, or chatter over rough spots.
I think you are right to go for a carving ski. Many rental shops push mid-fat or fat skis, but how many powder days are you really going to ski? Carving skis are probably going to be more fun and more manageable while learning.
I have really enjoyed demoing the products from Volkl and Nordica, and 2007 Salomon. They have had the above 2 qualities. Granted, I demoed high-end products, but for example I'd recommend trying something higher than the S1 in the Volkl product line, such as the AC2, or one of the lower end SuperSports, like the Attiva S4 (if you can find them to try). I really liked the Salomon X-Wing Tornado; it was a very easy to handle ski that had good hard-snow grip and and a nice stable (yet still lively) feel, so based on that I'd recommend trying the products lower in that line, such as the X-Wing 10 or Blast. Previous recent years of Salomon skis (i.e. 2005? Scrambler Hot) had a plastic-ey feel I didn't like and were more chattery. The Nordica skis I've tried were excellent carvers and nice and solid. I'd certainly recommend trying an intermediate model, though I'm not familiar with the specifics.
There are a lot of K2 skis out there for rental, but I found the Crossfire too damp and unexciting, so I have not tried any others. Not sure about edge grip compared to the above.
Some brands tend to be harder to find as rentals (at least where I've lived) so unfortunately I have not given some brands much of a tryout: Dynastar, Head, Elan, Fischer.