Firstly, if/when you're first starting to mail, buying a "database of millions" isn't the best way to hit the ground running as the biggest issue that you will have in the beginning is consistently mailing volume.
I would say that as a beginner, it would be worth spending more to acquire a smaller, more targeted list. I read above that you plan on mailing all types of offers, but surely the database you purchased is at least targeted in some way? Or is it just a "1 million usa emails" type of database?
Anyway, I will avoid further talking about data and get into some tips for mailing.
1) Yes, the first thing you need to do is clean the list.
2) Instead of sending out "relationship" building emails, personally I've found the best thing to do is send out a bunch of blind swipes designed to get opens. You can google for examples, but again it's niche dependant. You want to collect openers from your database because engagement is key to staying in the inbox.
3) You then focus on your opener list and start pushing offers.
Let's say that on your million list, you sent out 5 blind emails designed to be opened.
Bulk mailing depending on set-up and other factors, especially since you're a beginner, we can assume 1%-5% open rate however once you've got your openers, will be getting at least 20% open rates, smaller list sizes and better engagement scores.
Now you also mentioned you are paying someone to send the mails but when you mail yourself, you need to ensure that you warm up your IP's and just as important: you need to make sure your send domains have Good/High reputation (for optimum results).
Also, once you've got an opener list, you can start importing it into different ESP's as it will be verified active data.