I posted part of this reply on a different thread about the purse, but I think it applies here too, so I'm going to do a little bit of a cut and paste with new opinions thrown in.
I'm with the majority of the other posters on this thread: I would go with the city for your first b-bag. I personally am a big fan of the purse, but it is nowhere near as functional as the city bag is. I have owned both styles.
The first time I saw the purse in person I was shocked at how small it looked; I expected it to be much larger. I would not recommend buying the purse without being able to see it first-hand as I think that it looks slightly different in person than it does in photographs.
I'm not exactly sure what you are looking for in a bag, but in my opinion the purse is a more formal/dressier looking bag than the city is. You can dress the city bag up, but I don't think there is really a way to dress the purse down. I'd wear my city with super-casual clothes (like track pants and a t-shirt), but I'd never pair my purse with this ensemble. On the other hand, I would absolutely wear my city to work or out to a nice dinner and a night at the theater.
The one big plus on the purse is that the handles fit over your shoulder. The city does have the shoulder strap though so you can throw it over your shoulder as well. I can also wear the handles of the city over my shoulder so long as I don't have a coat on. The drop on the shoulder strap of the city is longer than the drop of the handles on the purse. The handles on the purse really aren't all that long though. I think that the top of the purse sits much higher on me than the top of any other normal "purse" style would. For this reason, I think the purse looks best with a form fitting coat or no coat at all. If I want to reach into my purse I have to drop it into the crook of my arm because there just isn't enough space between my armpit and the top of the bag to comfortably reach into it while it is still on my shoulder.
Even though the dimensions on the purse are slightly bigger than those on the city (length-wide and width-wise), the purse holds a lot less than the city does. The purse is quite flat, so you can't fit too much into it without making it look bulky. The purse is really a larger version of the first. The opening of the purse is also much smaller than it is on the city because the top sides are slightly tapered. As a result, the zipper does not extend all the way across the top of the bag. I find it much easier to stuff my New York Times into a city than into a purse. I can fit my 11" laptop into the city bag (although I would not recommend this because the bottom of the bag sags with the laptop in it), but I cannot even come close to fitting the same laptop into my purse. I can load my city up with lots of different essentials of varying sizes, but once I start adding items that aren't flat into my purse it starts to look bulky and awkward: it bulges and it looks silly and ugly under my arm.
So, if you are looking for a great everyday bag, I think the city is the bag for you; I don't think the purse is nearly as functional as the city is. I like the purse because it is a little dressier and more formal looking than the city. To my eye it is more structured and I am willing to give up a little functionality as a trade-off. I would buy the city first, and save the purse for a later purchase. These bags are highly addictive, so chances are you are going to want more than one.
On the subject of ink v. cognac, I can't really give a good opinion because I have yet to see the cognac in person. I do like the ink though and I have a bag in ink myself. Hope this helps. Good luck!