Which TTWin Integrator emulation do I use?

The emulation you need to use will depend on your host and the software running on it. For example, if you are connecting to an IBM System Z you would might use the IBM3270 emulation.

If you are connecting to a Unix system, there are a variety of terminals available. If you have an existing setup but you don't know what the terminal type is, enter env at the shell prompt. This should return, amongst other things, the TERM entry. This is the terminal type you are currently using.