gginnj:
huh...a pi would pull just about as much as a Nano or Micro?
No, a pi uses about ten times as much power. And costs ten times as much as the cheaper Arduino boards.
As your target application does not require USB connectivity, a (Pro) Micro does not include the USB interface and therefore uses just that little bit less power. In addition, it is available in a 3.3V version (with 8 MHz instead of 16 MHz clock) which suits powering from a lithium battery, and which the USB versions are not as USB operates at 5V.
This means you do have to use a separate USB to TTL adapter to program the Pro Micro only whilst you do the development. It also means that the Pro Micro is the smallest of the usual Arduino boards.
gginnj:
I want to create a water level sensor that will then take the voltage output of the sensor , run it through the D-A converter and then using a wireless transmitter (like a garage door transmitter) send the output.
I do believe you mean an A-D converter?
And a garage door control transmitter is designed to send security codes - you actually want to send data using one of the modules available for this specific purpose.
gginnj:
Essentially, it's two projects - one to read and convert the distance output and the other to send the data using the serial transmitter.
Well, one device to do this.
gginnj:
I was originally going to try this with a pi - but for this purpose, the power requirements of the pi would suck the battery much quicker - and I don't really need all the fluff of the pi for this what I'm doing.
You most certainly do not.
gginnj:
The Micro Board looked good for power usage, or should this be done with the uno board?
My other concern is that theft is a possibility - so I'd rather not sink a lot of money into each sensor - so the cheaper (inexpensive) the board - the better.
The UNO is often recommended for "beginners" but in fact a Nano on a breadboard is more versatile unless you wish to use pre-built "shields" which you do not appear to. And the Pro Micro is even more compact, you just need to connect the adapter during development. For final implementation, it is generally perfectly practical to use the Pro Mini as a very cheap module which you can mount on a perfboard or a custom PCB with your other circuitry.
For absolute minimum power usage, you need to learn to use the "sleep" mode and de-solder the resistor which feeds the pilot LED. You can still use the Pin 13 LED to indicate significant status.