Welcome! I just joined too, just got the phone yesterday.
I like Nesoid, Snesoid and Gameboid- they give you almost unlimited gaming for a fraction of the price of a usual homebrew app game and the free version works just as well, only without allowing you to do save-states, or basically saving even when you aren't supposed too. Although corporate ROMs are of questionable legality, homebrew games for the NES, SNES or GBA run fine and are perfectly legal!
I also enjoy Labrynth Lite. Great showcase of the Droid's tilting abilities.
An application closing device is generally reccomended, and although I use TasKiller (suggested by the Verizon store I bought my Droid at) Advanced Task Killer is generally suggested more by users, so I'm not sure which you should go for. TasKiller works fine for me.
I'm not sure there really is any app that makes it easier to use... what you may want to do on the Home menu is hit MENU>ADD>SHORTCUT>APP and add your favorite applications to the main screen. It's a lot easier at first to just hit the applications on the main screen instead of scrolling through a cluttered screen of random icons =P
All I can really say beyond that is just play around with it. It isn't very easy to start but is incredible once you learn the ins and outs of it. I was overwhelmed when I bought it yesterday and now I'm zipping between apps and messaging like lightning. A little exploring goes a long way!