For customizing your device, I fully recommend the following.
Some must have apps for me are Aviary for picture editing, Pandora for music, unless you want to give Play Music a try, which is AWESOME, and of course the android central app and android central forums app.
Yeah, don't try to go super crazy with customization right away, but figure out what you do/would/could find useful. As you have free time, look into some things, but I would hold off on any paid apps for customization until you know what's out there. Easy to pay for something, find out it doesn't do what you wanted or thought it did, and end up never using it (speaking from experience). Personally, I use a few added widgets, and that's about it. Most of the usefulness comes from organizing things so you know where they are & can get to the most used stuff quickly.
Start small and simple. Try a new launcher like Nova Launcher, which provides a stock Android look while allowing you to customize things (like removing the persistent search bar, changing scrolling behavior, etc.)
Look at the various theme packs for your launcher. Many of them are compatible with several (Nova, Apex, Go, etc.) and can quickly and easily give your device a whole new look with a few quick settings changes. Plenty of good free ones out there, don't pay unless you fall in love with something.
Check out new widgets for important info or things you use a lot, like the calendar. Personally I'm a fan of Beautiful Widgets for clocks and weather as it has a wide variety of downloadable themes, but there are a ton out there (HD Widgets is also good).
Download some new wallpapers, or live wallpapers for something fancy. Again there are a ton of options, and with a cloud service like Dropbox, Drive, or Box you can use practically any image you find on the web. Some will look better than others of course, but experiment. The various launchers usually come with some wallpapers, and have additional options for cropping and how your wallpaper behaves.
Once you're comfortable with all this, dive into the world of custom widgets. Things like UCCW, WidgetLocker, Widgetsoid, and Minimalistic Text all give you the power to make incredibly varied and customized looks for your homescreens and lockscreen. If you need ideas, browse one of the many homescreen threads here or on other forums. Most people are happy to share what apps, widgets, and wallpapers they used to achieve a certain look.