Email delivery platform with QB integration (MailChimp?)

I'm going to preface this by saying that I am a low code business user who wears many hats at our company. I have next-to-no knowledge about email marketing/communication, but here's my current challenge: 

We are a saas company that until recently managed all communications with subscribers manually via Outlook. Given our recent growth, we need to manage in a more programmatic way. 

There are two types of communication I need to tackle: 
(1) Marketing emails for prospective subscriber
(2) Welcome email + updates for subscribers

Currently, we maintain all of our CRM data in QB: Contacts belong to Companies who are subscribed to Products. Currently, if we need to send an email blast to all prospective clients for a particular product, we simply export a QB report and include everyone in bcc. This is very limiting: the emails aren't personalized, they often wind up in Junk mail, and email design is very basic. 

I really like the design capabilities of MailChimp, but I'm not sure how to connect our QB Contacts table to MailChimp's. I'm comfortable with Zapier, though for this use-case I would need to be careful with their "per automation pricing" (ie. it would be way more affordable to update MailChimp's contact lists once per day instead of every time a QB contact changes).

I've looked into Juiced's Quickbase Courier, but it lacks the analytics I need (for now, I would just like to be able to track bounce rates). 

I'm sure this isn't a unique challenge, so I'm hoping someone has tackled before!