1- that it only switches between applications and not open windows of those applications
Witch.
2- that when I stop on that application, it doesn't bring up the window.
Try Cmd-H to hide the application instead of minimizing. When Command-Tabbing back, the window will unhide. Minimizing on OS X is a mouse way to hide and unhide one specific window of an application.
This is an interesting UI decision, and I can see the reasoning on one level...but I still want to change it

Witch does indeed bring back minimized windows, and lets me switch between the windows of one application.
I think I might use this application enough to justify the (IMO) very steep price.
Keyboard Preferences is the right place, perhaps a picture will help.
I eventually figured out how to do this, and I really like how it behaves. I worry about whether other developers are consistent with their menu commands, but I mostly just need it in the browser.
It appears that the main thing I can't do with either this dialog or KeyRemap4MacBook is to modify actions that involve the mouse. For instance, Ctrl+click will not open a new tab, and I don't think I can change that...