One feature that could help is New feature: Scheduled machines
Otherwise, I’d say at least let one machine run on your app 24/7 so your cron run properly. You can use min_machines_running to 1 so no ping feature is needed: Automatically Stop and Start Machines · Fly Docs
As for the price, depends on your VM: Fly App Pricing · Fly Docs. A shared-cpu-1x with 256MB RAM for example would cost $1.94 for a full month.