I'd suggest that you go to the Market, perhaps on your computer for easier navigation and reading, start with the free apps, select what you might like, read the user reviews and stick with ones that are rated 4 or better. The newest reviews are important because they reflect the latest upgrades. Go to the Amazon Market; they have a different app for free each day that normally costs $1 to $5.
For starters, if I had a DX, the first app I'd install is SwiftKey, which has an uncanny way of predicting what you will type next (after it 'learns' what you normally type) and saves you a lot of keystrokes. Of all the weather apps, I like The Weather Channel best. I like GOSMS Pro for texting more than Handcent or the native texting app. ColorNote is an easy app for making lists and jotting things down. Ringdroid is a neat app for making custom ringtones. It's easy to uninstall an app you don't like.