I wish I was there to tell you to head east from the beginning. The little hills start pretty much right away as you head west, and the big ones are waiting for you about 8 miles down. And since that first section parallels a major four lane road for several miles it's not particularly scenic. It's a "get through it and onto the good part" section.
East, on the other hand, is directly down the old railroad right of way and basically flat (with some very gradual upslopes and downslopes) for 37 miles. It doesn't parallel any roads for miles and it goes through a very forested country in that section. Fall is a great time to ride through there. And about 7.5 miles from Rockmart you hit the 800 foot long Brushy Mountain tunnel, which is a memorable landmark and a trip to ride through. Turning around at that point and heading back to Rockmart makes a 15 mile round trip.
As to Coot's Lake, you might be imagining something grander than it is. Coot's Lake Rd crosses the trail there and there's a little lake by the road that has a little paid beach open in summer, but honestly it isn't a whole lot more than a swimming hole. The best thing about it is just down from where the trail crosses the road there is a gas station with a convenience store. If you're coming from the east, it's the first sign of civilization, and a place to buy a drink on a hot summer day, for many miles. It's 13 miles from there back to the Tara Drummond Plaza, which has a drinking fountain (and bathrooms) but no store.
Brushy Mountain tunnel (Take a look. I don't want to steal this person's picture but it's worth checking out. The tunnel is three stories high.)