Thanks for the mention of VNC Viewer. I've used it in the past on my Windows boxes as well as, if I remember, my old PDAs. Seemed to do a nice job then with not much overhead.
This has all been really great info and is going to help me. Deciding on the software is likely going to be an on-going process to see which, if any, of them give me more of what I need and might not have been able to articulate here. Thanks for all the details!