If you are running a script, you don't need a terminal to open or start a process, unless you need the process to run inside the terminal.
If you need the process to run inside the terminal, you will probably need some manual intervention to close the terminal. Most terms will allow you to execute a command by issuing some option like '-e command ' along with the command to open the terminal. Check the man page for the terminal. For example, I can issue 'gnome-terminal -e nmon' inside a terminal (or script) and it will pop up the gnome-terminal and start the process nmon, but (to my best knowledge) I will have to close the new terminal manually.
In the script, you can do this to run the process/command so that the script will wait for it to close/complete before continuing:
command -or- eval command
Or, if you want the script to continue without waiting for the process/command to close/complete:
command & -or- eval command &