It sounds like you are off to a great start here. However, as I am not a licensed insurance provider, I would suggest, if possible, consulting with the firm that provides insurance to your organization to get a professional opinion regarding which types of vendors require specific coverage.
Keep in mind that just because your vendor has insurance, it may not be enough protection for your organization. In some cases, you may want your organization named as an additional insured party. Vendors can extend their liability coverage to other parties, like clients, lenders, and joint-venture partners, by adding an additional insured endorsement to their policy. These parties must be listed on the endorsement and COI to be covered.
There are many good reasons to have your vendor add your organization as an additional insured party. For example, let's say your organization suffers a cyber breach but is not listed as an additional insured party? An injured party, such as a customer, might sue your organization for damages even if the vendor you hired was responsible for the breach. Due to the breach, you could be liable for any losses incurred.
It is possible for organizations to avoid filing claims under their own policies by being added as additional insureds, which places financial responsibility on the party that will most likely cause the claim. However, there are a few things you need to know before you become an additional insured. Ensure you have a clear understanding of the difference between a blanket additional insured and a specific additional insured, as well as the particular contract provisions that can further reduce your liability.
I hope this information is helpful, but I would love to hear ideas from other members as well.