I live in the Greenacres section of Scarsdale. We live very close to the Hartsdale train station though, barely a 5 minute walk, so we haven't had to park there. There are permits available for Scarsdale village residents, for $350 per quarter, and there is meter parking too. From what I gather your renewal is automatic, but I'd call to confirm. This website has the info:
Hartsdale Public Parking District
It is beneficial to get on in Hartsdale because you get a seat. A lot of the rush hour trains originate in Hartsdale, and by Scarsdale it's standing room only. (e.g. the 7:58 am train goes Hartsdale-Scarsdale-GCT)
We got a permit for Scarsdale when we first moved here but never used it so we didn't renew it. I believe it was around $1200 for the year at the Christie Place lot. Traffic is negligible driving down through Fox Meadow (pick a street or go down on the BRP), but the traffic in the village is terrible because of all the construction. So it depends on where you are going.
There is no bus on Fenimore, and actually, traffic is pretty bad on Fenimore at peak times. I've seen it bumper to bumper the entire way from Post Road to Hartsdale, in both directions (okay, that's rare, but it IS busy). However, if you're in Greenacres you can get over to Walworth and then you miss most of the traffic.
If you have any specific questions feel free to send me a message!