Congratulations, it sounds like you have a lot to celebrate. As others have said, it is a bit of a long trip from Poly to WS at Epcot. I know that with DME I have been told to expect 90 minutes from time of landing to getting to any of the hotels. If your flight lands at 5:30, I would plan to be checking in around 7:00. If you are not worried about going first to your room and refreshing, then you might just make it to a 7:50 reservation, but you would probably feel rushed.
If you decide to try for something closer to your resort, obviously anything at the Poly would be close. The Grand Floridian is within walking distance to Poly. Contemporary is along the resort monorail. If you still want to eat at someplace at Epcot, I think anything after 8:15 would give you time to check in, visit your room and make it to Epcot without feeling too rushed. Since it is your first visit it is likely that you will need the extra time.
As the previous posters suggested, if you decide to go to Epcot, walk from the Poly to TTC so that you can get on the direct monorail to Epcot. This site give a good overview on transportation options "
AllEars Transportation".
Also, make sure to look at the maps you can find in the link below so that when you get there, you know where you might need to go. This could be helpful if you try to get to a restaurant in Epcot the night you arrive. Knowing somewhat which direction you need to go before getting there should help.
WDW Info Maps
Both of us grew up living close to 
