Let's talk pricing.
At its core, Calendly is free to use (and the plan I use for now). You get 1 calendar that can be integrated with your existing ones, unlimited events, and your own Calendly link (e.g. calendly.com/prithvi-rakhyani).
Unfortunately, the free tier is limited to 1 event type. So if I have one 30-minute meeting configured, even though 1,000,000 people can book a meeting with me, I can't create another type of event (e.g. a 15-minute meeting) until I delete the 30-minute one.
The free version also includes (email) event notifications (whereas the paid versions even include SMS notifications). You can integrate Calendly to your website using pop-ups and embeds, as well as access to Calendly's email support.
If you want more, the paid version offers a lot. For $8 or $12 a month, you get more calendars, event types, group events, integration with hundreds of other applications, and even analytics. Check out their pricing page.