Need to create a drought-resistant yard; should I use bark or rock?

Do you have edging so the mulch does not wash away

first, plant drought resistant plants .. then you won't need so much mulch; Personally I prefer bark, shredded cypress, wheat straw, etc.as it will decompose thru the years and can be easily moved away to plant -- rocks, even over landscape barrier material will collect seeds/leaves/weeds and is a pain to keep nice without a lot of effort -- look into what will grow well in your specific area https://www.epa.gov/watersense/what-plant

That kinda depends on your budget and how often you want to reapply. Bark breaks down so it needs to be refilled or replaced more often

I am going to be working with a blank canvas so to speak. We are in a new build without landscaping.

Neither. Rock retains heat and will dehydrate anything you plant in it. Bark, well it just doesn't do anything. I would recommend using a good layer of mulch. Mulch will help retain moisture, shade the roots of plants and help to keep down weeds. Good luck!

You're welcome! Good luck!