1. Handcent SMS - absolutely must have
2. WeatherBug elite - widget is nice and make it worth the price, but WeatherBug is ok if you don't want to pay for a widget
3. Slacker or Pandora - whichever you prefer, I personally use both
4. AppAlarm Pro - alarm to wake up to slacker/pandora, worth the cost if you don't want to enable alarm every day
5. Google voice - no invite needed anymore, must have even if only for voicemail
6. Smart shortcuts - put your apps in folders without them all having the same folder icon
7. SMS wishes - schedule a SMS to send automatically at a preset time
8. A file explorer - I use ES File Explorer, but alot of people like Astro
9. Barcode scanner
10. Redboxer - great if you rent movies from RedBox
11. Cal Widget - if you want your calendar agenda on your homescreen, lots of sizes
12. RingDroid - if you want to make custom ringtones/notifications for free, super easy and works great
Those should get you started.
Also I prefer HelixLauncher2 over any other launcher or stock home. A lot of options, runs smooth, and has a 4 app dock at the bottom that you can customize
For a browser I prefer Dolphin HD
There are a lot of others I use, these are just what I think are a great start and games are a matter of preference so I didn't list any of those.
Welcome to Android and don't forget to hit thanks if this helped.