The starter solenoid should not be a problem for the standard push button switch, you may have a bad solenoid. When using the switch give it a firm push, if the contact is intermittant or weak, arcing/sparking will destroy it.
When switching inductive loads it's SOP to use some kind of arc suppression, but there is none on this switch. A simple diode or varistor would do the job.
If you use a relay as suggested by Mike, make sure contact protection is added or the relay contacts will not last long either.