First things first....
Since your kiddos are a little older, I would get on the website or get a disney guide (official or unofficial) and look through it and see what appeals to your kiddos.
We love both Epcot and Disney's Hollywood Studios (formerly MGM). In fact, we just came back from a quick overnight trip and only went to the Studios. We went to see Fantasmic the first night. The next day we had planned to go back and then hop to Epcot before heading home, but we never made it to Epcot. We got there just before rope drop and went in (since there were morning EMHs that day). While we were there, we won a dream and were allowed to stay in the park for 2 hours after closing and enjoy the rides. We left for a couple of hours to go play on the beach, but other than that, we were there the entire day and never got bored.
However, the Studios aren't for everyone, and many will tell you that it is a half-day park at best. Most people do love Epcot though, and there is a ton of stuff to do and see. Even if you just walk around, you take up a good portion of the day. Because of that, I would suggest Epcot to you. I think it has more general appeal.
As far as which one to do first, I think it depends. Are you staying on-site? If you are and are able to take advantage of EMHs, I would do that park on that day. If you are staying off site, it really is a personal preference. MK is Disney magic at its best. Some people don't really feel like they're at WDW until they see the castle. Others insist it is best to save it for the last day. It really is a personal call.