For the trip to SHV forum2233's recent report is very detailed and recent. You really should read it if you go for that route.
Bigal pointed out that the buses run from Chantaburi to Aran in Sakeow province. They actually stop at Aran bus station from there it is a 6 km motorbike or tuktuk ride to the border. Look for the Buriram bus at Chantaburi. Buriram is the line's terminus. Third class fan and 2nd class aircon buses service the route. Fan is no problem as the route runs thru lush forests and you get a nice breeze. Very friendly staff, working people who have nothing to do with the tourist industry. Nice crowd.
If you want to go by Pailin you need to get out about an hour north of Chantaburi at a crossing. The bus drivers know the spot and if they have problem to understand you people in Chantaburi bus station will help out. Cross the road as the songtaew to the border leaves there. You need to make it clear that you want to go to the border since driver goes to a nearby village and needs to make a small loop for you.
ALTERNATIVE: Aircon casino van to the border casino. Costs a little bit more but probably worthwhile.
After the border: Motorbike to Pailin. From Pailin to Battambang vans or public toyota taxis. I like the toyotas as they are likely to give you some 10-15 min along the way to take a quick look at three Khmer prangs right next to the road (100 meters off).
If the water levels allow, take the boat to SR, in case you have not done it so far. Very impressive, make sure batteries and memory chips are fit for the workload ahead.
I prefer the boat trip Battambang to SR and not the other way around. You see the river in the morning when it is less hot and have cooler temperatures at the lake later on. Make sure to bring a hat for the boat and the temples in SR.
Finally, I doubt that there is a direct bus from Koh Chang to SR. There is a direct ticket involving different companies and, I m prepared to place a bet, a series of scams. The latter include shitty restaurants, extra charges at the border, and a host of annoyances in SR on arrival. It is the same story almost anywhere in Thailand were private bus companies offer such services. Go to Trat bus station or to the one in Chantaburi and get a regular bus (in Trat it might unfortunately be a regular van).