Hey Josh- welcome to the sport!
My physique leaned up considerably when I started rowing (relative, of course, to what it was beforehand- I still love chocolate way too much to actually be considered lean). Some advice for your workouts:
Start slow and easy, and build your time, distance, and intensity on the rower up slow as well. Most runners have a rule of thumb of adding only 10% more distance a week, which seems to me to be a decent guideline for rowing as well.
As your body adapts to the new motion and fitness, be sure to vary your workouts. By this I mean do different distances at different speeds and stroke ratings. For example, starting with a warm-up, then tieing into a 5k, then finishing with a cool-down is a decent workout (especially when you're pressed for time), but you'll also need to add in workouts with longer distances (eg, 10k, an hour, etc). After a few weeks or a month or so, add in some interval workouts (eg, 500 meters hard, 2-4 minutes rest, x6). There are lots of long distance workouts and interval workouts to mix things up a bit (there's a "workout of the day" feature on the C2 website that's good for ideas, too!). The different workouts will challenge your muscels and cardiovascular systems in different ways, and also engage you mentally and keep things interesting. (Side note- interval workouts are best started after a while of building an aerobic base- the better your aerobic base, the more impact the interval training will have on your fitness and speed).
When you do your ab work, be sure to do some work on your back as well to keep things balanced. As goofy as it sounds, a good, basic yoga routine can be really good for a rower, both in terms of helping maintain flexibility and developing/maintaining core strength. (Secret confession: I have a yoga video that I pop into the DVD player and run through a couple of times a week- I actually made my husband promise not to laugh or he had to join me).
Finally, have some fun! The fish game you can download off the C2 website is fun and goofy, and good for the occasional "down in the dumps need a lift" warm-up. Like all good exercises, it'll take some time and consistency to see results - but you will see them.
Good luck and happy erging!
KateB