To climb routes you need shoes, a harness and a rope. If you've never been outdoors before, I'd suggest going with some friends or hiring a guide. Ask them why they picked their rope and what they think of it. Once you're ready to venture out on your own, it's time to buy a rope.
For your first rope, I'd recommend something on the thicker end. It will be heavier, but much more durable. The GriGri 2 works best with ropes up to 10.3mm, so I would recommend staying between 10.0 and 10.3mm.
The next consideration is length. The standard has been 60 meters for some time, but that is starting to shift to 70 meters. This is somewhat location dependent so ask around and check out the guidebook. Also remember that if you have to cut off some of the end of your rope, it's much easier to go from 70->60 instead of buying a new rope. If cost is a concern, go for 60 meters.
Dry coatings eventually wear off and they make the rope zip through belay devices. I'd recommend skipping the coating and using the cost savings to buy other gear.
Sometimes you can snag a Bi-Pattern rope for only a few dollars more than a standard rope, so it's worth checking out. The pattern never wears out and is easy to see, but there are other ways to find or mark the midway point.
Here are some searches to get you going:
Be sure to check out our full buying guide if you need more details.