If you have two partitions, they will show up as two volumes in the Startup Disk (Startup Device on System 6) control panel. One of your partitions currently has 6.0.7 on it. Install 7.x on the other partition and switch between them in the control panel. You only need a program like System Picker if you have one volume, but the partition will make Apple's control panel sufficient for this task.

Your choice of primary operating system depends on which programs you want to run. For maximum compatibility, I'd go with 7.x, but if you only need it occasionally, feel free to stick with 6.0.7 most of the time, especially if you prefer its simplicity and speed.