PO question: how to estimate ROI and prioritize advertisements for a product

Assuming you have a marketing department, I'd bring them into the conversation to help determine what channels may be the most appropriate for the target audience. 

There's also technology that exists to tie marketing campaigns to sales, conversion rates, etc so you can measure the success of the respective campaign. 

In addition, a technique such as impact mapping can be a powerful exercise here in order to map the business goal, customer goals, customer impact, and product backlog items together. 

How can you estimate the ROI and prioritize advertisements ?
Let's say you want to catch more children public. How can you say, ok with 10000$ we will cover a region, a state ?

Are you experimenting to find the right balance ?

Would it be more efficient to estimate, or to run a small advertising experiment and find out?

There are several campaign management suites that can be utilized for this purpose.

In addition to having multiple advertising platforms at one location, they also incorporate hypothesis testing for marketing campaigns. A/B testing, behavior testing, demographic distribution, geofencing are some of the tactics to run the primary campaigns for building better estimates. Nonetheless, your product landing pages also need to be tagged, crawled and optimized within the code for campaign keywords. You will be able to get pretty tidy insights regarding conversion rates per channel, CPC (cost per click), cost per add, sales funnel, demographic distribution, geographical distribution plus many more all at one go. 

Reach out to your marketing department. PO should never shy away from reaching out to marketing. In fact, marketing should be on its top priority contacts.