You asked about starter solenoids. If I were you I would buy two, keep a spare handy. I buy the two terminal type and they can be used on most all older model MTD's. Look at your IPL and get the correct part number then search on-line.
I've had a run of bad luck within last year replacing lawn tractor starter solenoids.
I've not found a good reliable generic type starter solenoids source yet.
On some of them the contacts stick and the starter keeps running and sometimes the OP is not aware of such until the engine is killed and the starter is running and then the bendix gear and or starter is ruined also.