If you have disabled Resume, you could set Settings > Shell > Startup > Run command to osascript -e 'tell app "System Events" to keystroke "f" using {control down, command down}'.
In iTerm you can make new windows open in full screen by selecting Preferences > Profiles > Window > Settings for New Windows > Style > Fullscreen. If you haven't disabled Resume, full screen windows are restored in full screen like in Terminal.
iTerm also has an option to use custom full screen windows that don't have animations for changing spaces, don't disable ⌘H, and allow placing other windows over them. There is a bug where the menu bar is always shown in restored custom full screen windows though. If you haven't disable Resume from System Preferences, you could also run defaults write com.googlecode.iterm2 NSQuitAlwaysKeepsWindows -bool false.