A friend of mine recently got an iPhone4 and we talked, as I have had mine since this past summer. I said I'd give her some information about the applications that I found most helpful, and figured I'd share the information here as well.
First, realize that many [not all] applications are not only able to work on the iPhone but also the iPad, although they may not look smashing on the iPad, they'll work.
Second, there are all sorts of sites online that provide suggestions for applications. Several which I find useful are: Lifehacker, Make Use Of and Mashable. There are no doubt others easily found through online research.
Third, the iPhone4 operating system has a great 'new' feature in it [which comes to the iPad apparently in November] - it's the ability to gather apps together into 'folders', which lets you have many more apps on your iPhone than the 11 screens will let you have normally. Using these folders is a great way also to organize your apps the way you want them, fairly simply.
My suggestion for the main [front] page is to keep apps on it which you use quite often. That will include all the Apple OS apps but in addition there are several that I find myself using over and over so they're on the Main page.
Two favorite apps are: AppBoxPro [you can get Lite free but for 99¢ you can get Pro, and it's worth it] and TripIt. In fact, having AppBoxPro lets you use its many functions within that one application and not need to resort to a plethora of others. AppBoxPro includes information on how much memory, storage and battery life you have. And it includes apps for other tasks: date calculator, a flashlight, holidays, loan calcs, pregnancy calendar, translator, tip calculator, and more.
TripIt is an online site where you can keep your trip plans and share them or access them on the road. I do not suggest you publish that information publicly, as a matter of privacy and safety. [You shouldn't telegraph to the world you're away from home, or going to a certain place.] But having only your family and closest friends able to subscribe to and be aware of your trip details is great. And when traveling, you can easily access all the details thru this one app on your iPhone, including directions, maps, lodging, meals etc.
I'll follow up this post with more in coming days on the other pages of my iPhone4 and suggested apps.