Automated Emails to Potential Clients Browsing your Website

Easy, set up a campaign (or rather a two-part campaign, as I'll explain) that triggers on web page visits, waits a reasonable period of time, checks that they did not check out a cart already, and then sends them the email.  These work best as two-part campaigns, so that you trigger the first campaign with the visit and a wait step, then hand it off to another requestable campaign that has a filter set up on it to cull out the ones that checked out a cart during that wait step before sending an email to the ones that didn't.

This can be achieved through a triggered campaign. 

The smart list is "Visits Web Page"  (select revelant page or "any")
Flow is Send Email
Schedule: Qualification Rules: Each lead can run through the flow every time

The original post does not mention whether a form was filled out or not.
If there was a form fill out, you can replace the vsiit web page trigger with "Form Fill Out", possibly refining with constraint "Web Page"

If there was no form fill out the email address was possibly collected through a cookie or website referral.
That may require careful consideration depending on the jurisdiction the lead is located.

Thanks!  Any suggestions for anonymous site visitors?

Anonymous can be tracked and scored normally. Campaigns will skip leads without an email address. It is normally collected through a contact form.

If the website you mentioned may have used a back door to obtain your email address if there was no form or any form of referral (that could include tracked links anywhere in the web).