1) Persistent disk is definitely the way to go if you want a root drive on which data retention is independent of the life cycle of any virtual machine. When you create a Compute Engine instance via the Google Cloud Console, the “Boot Source” pull-down menu presents the following options for your boot device:
- New persistent disk from image
- New persistent disk from snapshot
- Existing persistent disk
- Scratch disk from image (not recommended)
The default option is the first one ("New persistent disk from image"), which creates a new 10 GB PD, named after your instance name with a 'boot-' prefix. You could also separately create a persistent disk and then select the "Existing persistent disk" option (along with the name of your existing disk) to use an existing PD as a boot device. In that case, your PD needs to have been pre-loaded with an image.
Re: your question about cost of a 20 GB PD, here are the PD pricing details.
Read more about Compute Engine persistent disks.
2) You can serve SSL/HTTPS traffic from a GCE instance. As you noted, you'll need to configure a firewall to allow your incoming SSL traffic (typically port 443) and you'll need to configure https service on your web server and install your desired certificate(s).
Read more about Compute Engine networking and firewalls.