What are the most reputable email verification vendors? How crucial is this step in email marketing?

Do you have an idea of what kind of invalid emails you are receiving? That will help you determine which vendor is the best fit for you. For example do you consider support@, info@, or postmaster@ invalid, some vendors will weed those out for you? Or are you just concerned with making sure the email has an accurate Domain/MX Record? Will blocking SPAM IP addresses be enough to address your needs, if so you need a vendor who checks agains URI DNSBLs.
With that in mind, here's a good blog article about the top vendors. Best wishes!

https://www.formget.com/best-email-verification-services/

Most startups use Kickbox.io. If you need to verify 300K emails make sure you use their API to do so. You'll get shut off if you upload CSVs of email addresses.

Briteverify.com & Kickbox.io are definitely the two best IMO - cheapest, and lowest bounce rates (I've cleaned millions of emails with them).

There's quite a few in the market. Some are really expensive and most of them use the same techniques. I'd highly recommend to try MoonMail's tool which is pretty simple, straightforward, though you can only upload lists of recipients of up to 250 emails.
https://moonmail.io/email-verification-email-list-cleaning/