First thing you do is check that everything works. Plug something in to every hole and try it. Free support doesn't last forever. Press all the buttons and keyboard stuff. Try to start up from the recovery partition (shut down, then hold down 'alt' when powering booting back up).
I really like Maverick's full screen mode, and use 4-finger swipe to go back and forth between full screen apps a lot. You can change some of the gesture behavior in system preferences/trackpad.
I would've said use FireFox in the past, but not anymore. Safari is great. You can get extensions (using menu Safari->Safari Extensions... will take you there), I suggest AdBlock and ClickToFlash. You can enable ads on any website you want, and still get rid of the most annoying stuff. Oh ya, if you want to use flash, you actually have to install it. I wish flash were dead, but it's not entirely. But that's up to you.
smcFanControl is nice, but you don't really need it.
Manage your
apple id.
Locate lost devices.
If you're sometimes hooked up to a hotspot, and don't want to burn though your data with automatic updates, you can turn that off in system preferences/App Store. But there is a nasty gotcha, it doesn't turn off iTunes automatic updates, you need to do that separately in iTunes' preferences. Of course, you'll still need to update periodically.
Apple's office suite is free for new computers, it's okay. OpenOffice.org might be useful too, but nobody really knows what programs you need to use except you. Xcode is free, iBooks Author is free, do you want to use those? Who knows?