Hey Bob, I hope you are a Red Sox fan! (My hubby is from Winthrop and I became a Sox fan by osmosis.)
Anyway, yes, in Mesa there are several new construction communities. Those with the biggest selection of lots and floor plans include Lehi, Mountain Bridge, and Eastmark, and there are some other smaller builds going on. Depending on your tastes and price range, there are one-off lots ranging from middle-of-the-road to luxurious with views, scattered around the valley.
In addition to obvious preferences of layout and size, focus on energy-efficient construction. Some builders and communities focus on net zero costs for cooling over a year. The other thing to focus on is location relative to where you will be working, and commuting distance.
With your pets, how much wildlife, and what kind they will encounter, is a consideration on where to buy. If you have small dogs, avoid what we call view fences (just railings) that typically back up to a golf course or wild land. Reason: coyotes love to prey on small dogs and those view fences are an open invitation. if you have large dogs, don't worry about coyotes, but consider rattlesnake aversion training once you get here, especially if you like to hike.
Also, parks for walking the dogs and a not-too-oppressive pet policy in the Homeowner's Association are useful. The City of Mesa is very strict about dogs being on-leash at all times, but there are several off-leash dog parks that are popular, and no doubt there will be more in the future. Some communities tolerate informal off-leash gatherings but don't count on them as part of your buying plan.
You can probably tell I'm a dog lover too. I'd be very happy to assist you with your plans. If you would email me directly at firstname.lastname@example.org, I would be happy to set up a custom search for you. Just tell me a bit more about what you are looking for in terms of size, features, and price.
Ann Griffin, Realtor
Coldwell Banker Trails and Paths