So is the Compute Engine basically a VPS? If so, is it roughly equivalent to the base-tier DigitalOcean offering? Sorry for the stupid question; it just seems like I'm missing something!
A lot of the promise of GCE and GCP generally come from on-demand scalability, autoscaling, serverless, etc. Those become much more relevant as projects scale from a small set of fairly static resource requirements to larger and more dynamic usage. Take a hypothetical online retailer -- they might need few hundred cores at night while their users are asleep, a few thousand during the day, and tens of thousands on, say, black Friday. GCE lets you do that kind of scaling as-needed rather than having to provision far in advance (although there are pricing advantages if you can commit to cores and RAM over the long term).
(note: I work on GCE)
*subject to change
You can use the free tier of every product listed in conjunction with one another. No need to pick and choose.
I work for GCP and was the lead for the Always Free launch.
For some workloads, using Cloud CDN will save money, since cache egress is $0.08/GB (to North America.)
It's a dynamically scalable IaaS. You can treat it like a VPS (and that may be in some cases be cost effective for certain loads as one between the free quota and sustained use / long-term reservation discounts), but it's really more than that.