Hi Miranda!
Both weeks that you list are historically busy weeks for Walt Disney World, but the week after Easter will be slightly more crowded. With regards to the weather, the average daily high in April is around 83 degrees F, while in June it is around 91 degrees.
To maximize the number of attractions you can visit, especially the week after Easter, while minimizing the amount of time you have to wait in line, I suggest looking at the touring plans produced by the team that writes "The Unofficial Guide to Walt Disney World". They also have a website at TouringPlans.com. Their recommendations are based on a lot of math and years of collected data. As an engineer, I'm a big fan of their work. A good touring plan will help for either week you pick to visit.
To save money, you should consider staying in a Family Suite at
All-Star Music, a
cabin at Fort Wilderness, or getting two connecting Disney Value rooms. My favorite Disney Value Resort is
Pop Century; I would recommend getting two connecting rooms there for your family. Another possible way to save money is the Disney Dining Plan. You can get more information on the various plans
here.
Enjoy planning and write back if you have any more questions!