If you are able to come up with a number on the new build then you'll be able to compare apples to apples.

2) Are there any legal time limits with how long I have to own it before I can rent it out, or anything I should watch out for like that?

Any "lead" from your realtor is also going to be seen by every other "investor" who watches flip or flop and attended a seminar. 

have a few more space heaters ready to go if things get really cold.. watch out for plumbing.. you might want to keep water flowing a slow drip.. 

The only thing I can think of is to simply watch for obituaries in the paper, and first look up whether or not the deceased owned property, and then go to the courthouse and to search their system. 

For 2016, these were the top 10 real estate markets to watch.https://www.trulia.com/blog/10-hot-real-estate-markets-to-watch-in-2016/They looked at five metrics: strong job growth over the past year, low vacancy rates, high affordability, more inbound home searches than outbound, and a large share of millennials.

I want to be able to travel and give them experiences outside of what is familiar, as well as spending the time to watch them grow up.

Thanks Kurt, I did get a referral from @Dave Foster  @Dave Foster who setup a watch for me.  

Perhaps you could offer some labor in return for the privilege of watching the process (demo, painting, landscaping, etc.).

So many watch these flipper shows on TV and get crazy ideas from them.