Regarding the screenshots, I find that 90% of the time I'm taking screenshots it's to show somebody something, so I really like CloudApp. (getcloudapp.com) You do the usual shift-cmd-4, but instead of copying the screenshot to the clipboard it uploads it to their service and copies a link to the clipboard. On top of that, their site is really clean.
I like Skitch.com, similar idea, but it lets you choose what you want to take a picture off, and provides a basic image editor (handy for adding annotations, highlights, etc.) before upload.
Paintbrush makes for a good free image editor (http://paintbrush.sourceforge.net/) — I use Pixelmator as an almost-Photoshop replacement, but the former is good if you want something really light.
Native shortcuts to take various screenshots (unrelated to anything, but so useful and cool): http://guides.macrumors.com/Taking_Screenshots_in_Mac_OS_X
* Sparrow http://sparrowmailapp.com/ - Gmail done right
* TextWrangler http://www.barebones.com/products/textwrangler/ - Best text editor, for any purpose and free
* Pixelmator http://www.pixelmator.com/ - Mac equivalent of Paint.NET except it's not free. Worth it though!
* Transmit http://www.panic.com/transmit/ - FTP, SFTP, you-name-it client
* LittleSnitch http://www.obdev.at/products/littlesnitch/index.html - Software firewall for when you want to block certain apps outgoing web requests
Enjoy your new Mac!