Remote connection from pc to mac?

NoIP's DNS updated app is available for OS X - there's a GUI version and also a daemon that will run in the background.

With regard to remote desktop, OS X supports VNC out of the box - you just need to enable it - open system prefs/sharing. Go to screen sharing, enable it and click the computer settings button. Check the VNC box and enter a password. Bingo =]

I use this system to control remote Macs on a daily basis. By the way, you can also do this the other way around - MS RDC is available for OS X, but better yet, grab CoRD, which is an open-source equivalent - works real well.

Enjoy your new Mac!

 

I use the free version of logmein.com
it's really fantastic and if your IP happens to change in the middle of the day, like mine does once a year, it won't make a difference, since it follows your connection.

Edit:

it's web based and runs your desktop in a browser very effectively