I am also planning a honeymoon!
For where to stay, I would see what is available when you can book.
For attractions, you will want to try to get fast passes. You can book them online 60 days out if you stay on site and have your hotel booked. If you don't do it early, some of them won't be available later. Check out the Theme Parks and Attractions thread and mesaboy has a thread that explains fast passes really well.
Our must-do attractions:
- Wishes Fireworks in Magic Kingdom
- Illuminations Fireworks in Epcot
- Fantasmic in Hollywood Studios
- Rivers of Light in Animal Kingdom (This is new and isn't completed yet but I have read it might be for spring 2016 so maybe do some research)
- Space Mountain, Splash Mountain, Big Thunder Mountain Rides in MK
- Expedition Everest, Kali River Rapids, and Safari in Animal Kingdom
- Rock n Rollercoaster, Tower of Terror in Hollywood Studios
- Soarin and Test Track in Epcot
- Waterparks- Typhoon Lagoon has an awesome wave pool!
- World Showcase (Eat, Drink, Tour Shops) in Epcot
For dining, I would see what is available. You can make dining reservations now online. Are you planning on getting the dining plan? The standard dining plan gives you one table service meal and one quick service meal with one snack per day. Some say it isn't the best value but we like it because then food is paid for upfront. I would try to book dining reservations that are close to the park you plan to be that day. Some that we have enjoyed or want to try are Ohana dinner, California Grill, Be Our Guest, Coral Reef Restaurant, Brown Derby, and Beaches and Cream but those might not be available as you can book reservations 6 months in advance.
For transport, I think Disney makes it easy! At your hotel, there will be bus stops and usually one bus goes to each park. You will see the signs that say which bus to take. Other modes of transport are monorail and boat. The monorail loop from Magic Kingdom goes to Magic Kingdom, Contemporary, Transportation and Ticket Center, Polynesian, and Grand Floridian if you want to check those resorts out or dine there. There is also a monorail from the Transportation and Ticket Center to Epcot. There are boats in the Epcot and Hollywood Studios area too but you will likely be using the bus often if you stay at a moderate.
Just for fun, I will plan a general trip during your dates that we would do but your desires might be totally different! There is a blizzard outside so no I don't have too much time on my hands but I am stuck inside

A lot of these restaurants probably aren't available less than 6 months out but you can check online for cancellations, book restaurants in the parks that are available, or eat counter service. While the plan seems detailed, you will want to make sure to have fast passes and dining booked which means knowing what park you will be at for the day.
I used this link to see where to go each day:
http://www.easywdw.com/easy/calendars/april-2016-walt-disney-world-crowd-calendar/
April 3: Magic Kingdom (good place to start your trip and its recommended according to easyWDW crowd calendars)
-Arrive at resort
-Pool Time, Explore Resort
-Bus to MK
-Monorail to Polynesian
-Dinner at Ohana 6:00pm
-Magic Kingdom
- Fastpass Space Mountain 8:00pm
- Fastpass Splash Mountain 9:00pm
- Fastpass Wishes 10:00pm (gives a good location to watch it but don't need a fastpass to watch wishes)
April 4: Hollywood Studios (recommended park)
-Animal Kingdom in morning if you want to go to extra magic hours (less crowded because only for onsite guests)
-Pool Time
-Bus to DHS
-Dinner at Brown Derby Lounge (no reservation needed)
- Fastpass Rock n Rollercoaster 4:00pm
- 2 other fast passes but I don't have any recommendation
- Fantasmic 8:30pm
April 5: Epcot (Has extra magic hours at night... will have 9-11pm only resort guests)
-Pool or Waterparks
-Bus to Epcot
-Dinner at Coral Reef Restaurant 6:00pm
- Fastpass Soarin 7:30pm
- Fastpass 2 other rides of your choice
- Test Track during Extra Magic Hours 9-11pm
April 6: Magic Kingdom (Has extra magic hours at night starting at 10pm)
-Pool or Waterparks
-Bus to MK
-Dinner at Be Our Guest 7:00pm
-Fastpasses for 3 rides haven't done yet
-Stay for PM EMH
April 7: Animal Kingdom (not recommended but haven't been there yet)
-Morning at Animal Kingdom (doesn't currently have a night show rivers of light yet but might for your trip)
- Fastpass Safari
- Fastpass Kali River Rapids
- Fastpass Expedition Everest
-Dinner at a resort, the boardwalk? California Grill? Maybe go to Epcot Again?
April 8: Epcot (recommended park)
-Pool or Waterparks
-Bus to Epcot
-Dinner somewhere in World Showcase Epcot
-Drink and Eat around the World Showcase
-Illuminations 9:00pm
-Fastpasses for whatever haven't done yet
April 9: Whatever Missed
- Go wherever you feel you've missed out
- Fly home