From Gatlinburg to the top the gain is just about 5000'
Depending where you start it will be 23 or so miles each way (thats the town/park border distance; Sugarlands Visitor Center would be around 21 miles; where are you staying? )
Average grade is 4.6%, max is 8%, and not for long on that as its the section by the Chimney Tops Trailhead parking. The toughest part is from not far after Sugarlands up to the Chimney Picnic area, then you get a very brief break, and then its pretty tough to the 360 degree loop (just past the Chimney Trailhead); from there to Alum Cave is pretty easy and then it kicks up to Newfound Gap (5-6%) but it is very scenic. The last 7 miles to Clingmans is 3-4%. You actually get a mile downhill near the top before the final climb. Its actually the easiest section.
I usually leave by 8am so I'm at the top by 10:15 or so (its 26 miles each way from our house). I wouldn't do it mid day on a Friday or Saturday. During the week, you can go almost anytime but I still think the earlier the better. The tourists don't get going until 10am. They start in on the pancakes around 9am and eat for a good hour.
I do check the weather carefully. It can be sunny and warm in town and blustery and cold at the top. The temps can be 20 degrees cooler. Usually its 3 degree drop per 1000' of ascent. I usually have arm warmers just to be safe and maybe a wind vest. It was 50 at the top yesterday and 80 in town. I did it in short sleeves up and down and felt fine. Riding down even in the summer in the rain can be really cold so avoid riding if there is a chance of rain.
They sell bottled water at the top and some chocolate bars but thats it. There are composting toilets also. You are not allowed to ride the last .5 to the tower during the tourist season, April-December. Too bad as its 15-20%....its a killer!
I've never had an issue with cars on the way up. Most are passing pretty slowly. I do swing through the pullouts if I have cars behind me.
The descent can be dicey. I prefer to be behind a group of cars rather than leading but if leading I just go for it. I can go 35+ most of the way which is the speed limit. If needed, I use a pullout and let them pass. In all the years doing this ride (1993 was my first trip up, I think) the only issue I've ever had was a month ago when some idiot decided I was going too slow (35 mph, and I was following a car) and he passed me close enough that I knocked in his side mirror with my watch on my wrist. I like to think he was a lone idiot. There are two tunnels (check for debris in the downhill lane on your way up) and those switchbacks you rode on the way up will come at you very quickly on the way down.
I would say that is one of my favorite rides anywhere. When I'm really motivated (2-3 times per year) I go to Clingmans and then drop down to Cherokee and then ride back up and over. Its 100 miles with 10,000' of climbing. Its about 6.5 hours on the bike. The ride along Little River Road from Gatlinburg to Cades Cove is also outstanding. They are paving parts of that road so it may get backed up.
I attached the elevation profile. Ignore the climb at the end. That is Cherokee Orchard and Roaring Fork Motor Trail. Short, but wicked with slopes hitting 17-20%.
I have always used a triple or compact gearing. You don't want to do these with a 53/39 front and 12-23 rear. My triples are 53/39/30 with 12-25 and my compact has a 30 front with 28 year. you want to be able to keep up 85 rpm's. If your pushing the 70's you'll tire out quickly.