Best program for remote desktop?

Microsoft's Remote Desktop Connection for Mac maybe?

Free to download from Microsoft's Mac software area.

Connection to Windows, I agree with the recommendation of Microsoft's RDC for Mac:

http://www.microsoft.com/mac/downloads

Not only free, but it's seems to be the most trouble-free compatible RDP for connecting to Windows. No problems with foreign keyboards, cutting and pasting into and from the connected computer, for instance. The speed's gotten a lot better on OS X over the years.

If you're connecting to other operating systems, then there are other and often better choices. I haven't found one program that does all the protocals/OS (Windows RDC and VNC to Linux and Mac) equally well for my purposes. It would be nice to have a single console to connect to them all, but not at the expense of functionality and compatibility. I use one program for each OS.

Mac to Windows, use the above mentioned Microsoft Remote Desktop Connection, or CoRD

Mac to Mac use Screen Sharing, it is based on VNC, but Apple's client and server when talking to each other is better than generic VNC. If you are connecting Mac to Mac over the internet, then use the Back-to-My-Mac feature in iCloud. On the same LAN Screen Sharing is easy.

TeamViewer.com is good at remote connections across the internet, and it is cross platform.

LogMeIn is OK, especially if going from Windows via Internet Explorer as it then uses DirectX enhancements to make the client fast. Going from a Mac via Safari to a LogMeIn system is OK at best, but not all that great (TeamViewer.com is better - personal opinion).

If you have to go from Mac to Unix/Linux systems, then look at Chicken (formally Chicken of the VNC), or JollysFastVNC. These VNC clients will play nicer with non-Apple VNC servers than Apples Screen Sharing VNC client.

If you have to go from Windows to Mac, then you need a VNC client, and you may or may not experience problems with the Mac VNC server, as it does not always play nice with 3rd party VNC clients. If you have the need, and TeamViewer.com or LogMeIn.com does not satisfy your needs, then you might look at the Vine Server (aka OSXvnc) as it does play nice with 3rd party VNC clients.

There is nothing magical about the Apple Remote Desktop with respect to screen sharing. As you have figured out it is for managing a class room or office of Mac, besides that it does not offer that much for a single user (or even a family where there are only a few systems).

My favorite Mac to Linux/Unix view is RealVNC.

You can try using gosupportnow (www.gosupportnow.com) remote support tool in order to remotely access computers from anywhere. It works on both MAC and windows PC.

Teamviewer?