CRM for Inpatient Rehab Facility?

Hi! I've spent hours down the rabbit hole of finding the perfect CRM for my work and I'm still struggling. One of the key features I want is to have 3 users with 3 Microsoft Outlook email accounts connected to the CRM and have 2-way sync with the accounts so that if one of us is out of office, we can see the other's email.

1. This is for an inpatient rehab facility (healthcare)
2. It is small with one outreach person and 2 people doing intakes/admissions – challenge is to manage incoming communications within the team and prompt follow-up on inquiries. It would also be nice to send bulk emails from the CRM.
3. We get inquiries through our website, calls, and from referral partners

Everyone in this industry uses Salesforce but this is a small, new organization so the cost of $6,000+ for implementation/customization and the overall cost is way too high.