I'm looking for a smallish (~40 in) TV with Android TV built in. I'm having a hard time tracking this down as all the Bravias and Aquos are larger TVs and are quite expensive. The low cost Hisense and TCLs generally use Roku TV. Obviously, i can always go with a Mi Box paired with a cheap TV, but for useability reasons, I'd really prefer an all-in-one solution like the Bravia TVs.
Define low cost?
Not sure your use case here so this opinion may change, but it would seem to me that your best bet may be to go with a cheap TV paired with a Mi Box.
That way if you upgrade to a bigger and better TV you can just move you Mi Box over to it without any worries.
The 40" version of Vizio's E series is under $300. Doesn't have Android TV, but you can pair it AirTV for $100 (or $130 if you want the OTA channel adapter bundle), which comes with a remote that controls TV power and volume as well as Android TV functions.
As others have said, I can't in good conscience recommend buying a TV with Android built in. Dollars to donuts, the "smart" part of the TV will be antiquated before the screen is, and you'll be stuck having to shell out another $400+ to update (rather than ~$100 to get a new TV box).
Leeco 43 inch with HDR have decent reviews fits all of your requirements
http://www.lemall.com/us/leeco_tv/index.html