How I can unminimize windows from an application using a key combination?

I'm from the same boat;

the best native keyboard-only I've found is

1. CTRL-DOWN-Arrow; (you enter app expose)
2. DOWN-arrow; (if there are any minimized windows, this'll put a cursor on one)
3. LEFT-arrow/RIGHT-arrow (to select from multiple minimized windows) or hold OPT if you want all of them restored.
4. RETURN

alternative step1: getting into app expose before you've alt-cmd'ed to an app:

with CMD still held down, (the task switcher is visible) tap DOWN, or UP, or 1 (now in app expose)

The above shows only one app's minimized windows at a time; for selecting from any minimized window regardless of app, CTRL-F3 moves focus to the dock, and you can arrow left to get to the minimized list.

if your CTRL-F3 instead shows you the app-expose, try FN-CTRL-F3. (In my settings/keyboard, I've flagged "Use all F1, F2, etc. keys as standard function keys")

Some apps have specific alternatives; I use Terminal's CMD-window_number, which unminimizes and focuses that window.

Take a look at tip #10 on http://www.macworld.com/article/2048857/10-tips-for-managing-minimized-windows.html -- that did it for me.

Essentially, you use ⌘ Cmd+Tab/~ as usual, and for minimized windows, hold down the ⌥ Opt key before releasing the ⌘ Cmd key, and the application opens as you last minimized it.

If you want to unminimize ALL windows (not just from one application), you can create the following Automator service and assign it a hot key.

In Automator, create new service

Give it one action: Run Shell Script

The shell script is this:

killall -HUP Dock

This will kill the Dock process (which will then respawn), in the process liberating all windows that have been minimized into the Dock.

Save the service, then use System Preferences to assign a shortcut key to the service.