I am looking for a way to start Mirc when Windows starts up and place the icon in the system tray. Is this possible?

Place a shortcut to mIRC in:

c:\Documents and Settings\your_login_name\Start Menu\Programs\Startup\

Then, go into mIRC... Alt-O > Display > Options > Tray...

Check the boxes for minimizing on startup and for placing icon in tray when minimized.