Don't sweat it. I didn't get my first smartphone until December, also an iPhone.
PlainText and DropBox were the first two I got. They're free and the easiest way to store simple text files on a server that can be used on any platform (Windows, Mac OS X, iOS, Android). But PlainText really is plain text, so no formatting, no bold, no italics.
Adobe has a free Acrobat app for reading PDFs, which comes in handy.
If you want to sync your bookmarks but don't have a Mac computer to sync Safari OS X with Safari iOS, there's a Google Chrome browser. Set up a gmail account, and it keeps bookmarks updated no matter if you're on the smartphone or a computer. If you do this much, get Google Maps. Sign in with the gmail account, and you can keep bookmarked map locations, etc. There's also a gmail app, but Apple Mail is fine as it is.
Weather Channel has a lot more info than the Apple Weather app. Free.
Ookla has an app called SpeedTest, which lets you check your connection speed (doesn't matter if you're on wifi or wireless data). Also free.