Sounds like you have a good sized dining room so I can see your dilemma. The simple answer would be to use a tiered or linear chandelier with multiple bulbs. They will each be rated for 25 or 40 watts, most likely. Figuring total wattage revolves around the type of activity you will do in a room. Ambient or general lighting requires s.f. (324 in your case) x 1.5 for wattage. Task lighting is 324 s.f. x 2.5. Dining is not considered task work. However, we've all been in a restaurant where you could barely see what you were eating (!). I'd err on the higher side because you can always add a dimmer or swap the bulbs out to lesser (but never higher) wattage than recommended.

Another thought is to add 4" recessed can lights around the perimeter of the room for additional ambient light. Good luck!