I have been monetizing purchased data for the past 16+ years.
Not knowing anything about the data, I can just tell you how I do things.
CPA networks is the easiest way to go, as you can get offers quickly.
With purchased data, it's all about promoting free offers that have mass appeal, as you will get much higher conversion rates than typical offers that require purchases. I heavily promote PPL(pay per lead) offers, free sign-ups and free trials(+s&h). While free trials aren't really free, the users is usually getting something that would normally have an upfront cost of like $50-$60 and is just pay $4.99 or so in s&h, which they would of had to pay anyway, so they can still convert pretty good. I also promote a limited number of offers that require an actual purchase, but again it's always about mass appeal existing or it solves a house is in fire type problem.
Next would be to try and get set up direct with the owner of the offers. You will almost always get a higher payout and if you can produce volume, you can potentially get your own landing page and creatives, so your not sending what everyone else is. Sometimes you can even do this through a CPA network.
Last but not least is to develop your own PPL offers. Then you get the highest payout of all and you get to monetize all the thank you page traffic as well. However, this would require the most work and have some higher risks and for most in the business, it's not worth it to them.
Finding the best offers is all about testing. You also want to test the same type of offers against other of the same type, once you have something that works. I have seen huge conversion rates differences and had I not tested, I would of left a bunch of money on the table.
Purchased lists will never be as responsive as lists you actually developed yourself. So you always want to be segmenting the openers and clickers, so that your creating smaller, but much more responsive lists. That way you will eventually send less and make more each time you mail. Also, it improves your engagement , which will improve your IP reputation.
You also want to be segmenting based on what the offer was so your building targeted lists. If the data is already targeted you may want to test offers based on it in addition to the free stuff. Even if it doesn't perform the greatest, but you can get a lot of slicker, it's possible you could turn it into a solo ad business. However it's a lot more work than just sending offers, as you need to find buyer that will pay you to send offers.
All the above is the easy part as you first need to be able to mail it. Your going to want to get rid of all of the bounces first and clean it of known complainers, spam traps, etc... Since the data isn't fresh, sending with autoresponders may very likely be too costly and they don't tolerate a lot of complaints. SO you may l want to set up your own servers/IPs and have a good mailing platform to send with, but you need to know what your doing.
Feel free to PM me if you need advice.