Early June is fabulous. The earlier the better. I usually go the first week before the schools let out. There are grad nights however most Thursdays where the park closes early so the grads come in and take over the park for the night. I generally make that day a day where I go to Universal or do something else. Also park hours are extended so during the week the park closes at 11, and midnight on weekends, and all the shows like the fireworks, fantasmic, etc. will be in full swing as long as they arnt on refurb. But most refurbs are done before the summer hits, so unless something expected goes down your gonna be able to see it all.
I would say for your first time, especially in early June make sure you have a 4+ day hopper. 5-6 days are probably best. We had a 6 day the first time and we saw most of both parks, but not everything. You will find your favorite things and keep going back.
As for hotels, if you want to stay offsite you will find some good budget friendly hotels directly across from the main gate. Here is a map. Look on the right hand side. Anything between The Howard Johnson and the Ramada Main Gate is exceptional. Its directly at the Disneyland crosswalk or a 2 minute walk away. If you stay at hotels off this strip, you may have to use shuttles and its just a hassle in my opinion. I have stayed at the Howard Johnson, the Carousel, and the Tropicana, and a friend of mine stayed at Park Vue. My favorite was the Tropicana and Carousel. But others on here would rant and rave about the Howard Johnson.
http://anaheim-attractions.10-best.info/disney_map.pdf
As for dining plans... No its not like WDW where there is one. However there are Character meals that you can make reservations for (Starting at 60 days prior to your vacation). Both parks also have some nice places to eat, and Downtown Disney also has some wonderful restaurants. Here is a link to both DTD and the parks.
http://allears.net/dlr/din/menu/menus.htm
But if you stay on the harbor strip, there are restaurants all around the hotels. Dennys, Ihop, Millies, Mimis, Tony Romas, then there is the Anaheim Garden Walk with the Cheesecake factory, Bubba Gumps etc.