Best way to organise small business? CRM maybe?

I have recently been tasked with managing a team of 5 people who are all “venue bookers”

They work for a charity fundraising company and need to book venues such as shops and retail parks for the fundraisers to attend

They currently use a Google sheet that essentially has a list of all supermarkets in London, and another Google sheet which has all of the weeks of the year (like a calendar) with all of the venues that are booked for that week

The data is chaos, with notes not being updated the system is flawed. So the team are chaotically calling random stores with no knowledge of our previous contact with this store or who was spoken to.

What system would work best to integrate into this team whereby we can store all of the contacts for each individual store, updates notes which are visible to all users and a real time calendar that allows your to book these stores/contacts into a calendar system which is accessible by everyone?

Is a CRM of some sort my best option?

Any advice appreciated