Well, lucky for you they've given you your buckets :)

But, first you have to clarify the objective. So, what do they want to achieve with these acquisitions? Are they trying to acquire companies within their existing industry so as to reduce competition? Are they looking to acquire companies with knowledge they don't have? ARe they looking to vertically integrate? Horizontally integrate? Perhaps most importantly, are they prioritizing topline or bottomline growth? Finally, what's the budget? I.e. how big can these companies be?

Clarifying the exact purpose is incredibly important, as you cannot identify, screen, and prioritize if you don't know what you're looking for!

Let's assume you've asked this in the case. A quick and dirty approach would be

Identify

• Look at the "world of" targets (consider below approaches)
  • Look in public sources for companies that have said they'r looking to be bought, or those that might want to be
  • Reach out to the local network to find potential targets
  • Hire a PE firm
  • Etc.
• Once one or many of the above approaches have been selected, we can get a list of possible targets

Screen

• From this list, we need to first eliminate anything that doesn't fit (i.e. doesn't meet table stakes). This could be
  • Too big
  • Too expensive
  • Doesn't address key objective/needs (clarified in the prompt) (i.e. not in an interesting industry, etc.)
  • Not

Prioritize

• We should have a shortened list now, but we need to figure out what matters (relates to above clarifying question)
• We need to pick the top 3-4 things that matter, rank them, and use those as selection criteria. Some of these could be
  • Positive cash flow
  • Genuinely interested seller
  • Fits our market
  • Fills a hole in our existing capability
  • Reduces competition
  • Gives us a new customer base
  • Is a valuable brand
  • Strong IP
  • Culture fit
  • etc.
• We can then rank the companies across these criteria to make a shortened list of ~10-20 to approach seriously

To get the above information/data, we can:

• Request income statements, balance sheets (or, if they're public, find them online).
• Talk to industry experts
• Speak with company contacts
• Speak with company customers
• Review government industry reports

This isn't the full answer, so feel free to reach out to talk about this in more depth!