Kimberly:
To me, a "good time" to go to Disney World is when the weather is cool and the crowds are few. Unfortunately, you will find neither of these the first two weeks of June, so either week should do.
The major difference between the
Beach Club and the
Polynesian is in the theme park they sit nearest to: Beach Club is at Epcot's International Gateway and the Polynesian lies directly across the Seven Seas Lagoon facing the Magic Kingdom. If you think you'll find yourself visiting the Magic Kingdom more, the Polynesian would get the leg up. If you want the convenience of being within a 5-minute walk to Epcot or 15-minute walk or boat ride to Disney's Hollywood Studios, Beach Club should be your choice.
You can see fireworks while at both resorts, but the Polynesian's are more spectacular. Because it's June, you'll want to take the pools into consideration. The slide at the Beach Club and its sandy-bottom pool keep my kids' interests more. In addition, the lights and outside sights of the Boardwalk at night can be enjoyed while you stay at the Beach Club, and depending on how many people are in your party, you may find that the bathrooms at Beach Club accommodate larger parties. Its vanity sits outside the bathroom while the Polynesian's is inside.
But the deciding factor may be that presently the Polynesian is under construction in its pool area and main lobby building. In my opinion, I'd wait to enjoy this resort once it's completely remodeled.
Wishing y'all a magical vacation!
Whitney