Assuming it's an old school wired car, the start position on the ignition switch will deliver volts to the starter solenoid, and that in turn is really a relay, as it makes the big current supply to the starter motor.
No idea whether it's a separate solenoid or integral with the starter motor on your car, but I did have a separate solenoid commit suttee. The fault was diagnosed without me needing to get a voltmeter out as it was all blackened and charred!
I've also had a starter brush stick which caused a failure in hot weather (at a Mog do - in the middle of a gymkhana). That was easily, if messily fixed, removed starter, took it to bits, exercised the brush holder, put back together and it worked for years afterwards.
Both of these faults were marked by the lights not dimming which shows the starter is not taking current.
Personally I'd not be changing the ignition switch without evidence. Got a pal who knows their way around electrics and know how to use a voltmeter/multimeter?
