Powering Arduino Nano, ESP8266, and small motors

I'm looking for some general advice and/or specific recommendations for a project I'm working on - animatronic Halloween decorations. I'm fairly new to Arduino and hobby electronics in general, so bear with me!

The general premise is that I'll be using a Arduino Uno with a DMX Shield (RS485) and ESP8266 connected to either a hardware or software (USB dongle) stage lighting controller. Upon receiving the appropriate DMX signals on the designated channels from the controller, the Uno will transmit over the ESP8266 to multiple remote Arduino Nano's with their own ESP8266's. What each one does, I'm still planning, but I know I'll at least be using some small motors (whether DC, stepper, or servo) and perhaps some small speakers, too. But because these units will be remote and living outside for the day of the event, I'll need to be operating them on batteries. I need to have them fully awake and ready to receive the WiFi signal to then actuate the motors and speakers, since this will be happening in sync with other DMX-controlled stage lights. I anticipate that I'd like to have them operational for about 45 seconds at a time every 10-15 minutes for about 8 hours.

So finally, my question is: What would be the best battery configuration for these remote units?

Size and space are fairly open as long it's smaller than a 12V car battery. And I'm more than willing to hit Buy Now on the South America River for some additional parts. I do have a few buck step-down converters, plenty of AA and D batteries and holders (my first guess of a solution) and a few 7.2 V RC car batteries. LiPo's/18650's terrify me for this kind of stuff, but if that's the best option, I'll consider it.

Good advice is greatly appreciated (and I'll probably need to follow up for specifics!)

Is there a particular reason you want to use esp8266 modules for the communication? WiFi is not low power, and I don't see a need for its advantages here. I recommend choosing some other RF protocol, one that is low power, low data rate and has the range you need. LoRa is one possibility, but there may be others which are simpler to use for a beginner, for example HC-12 modules.

OK, looks like it is then a Lead-Acid "gel" cell of about 8 AH capacity, recharged daily. Or a LiPo pack as you would use for a moderately large model, again recharged daily or possibly every 2 or 3 days.

Are these not LiPos?

The only real reason I had selected this option is because I already had a few of these chips laying around. I'm not familiar with LoRa or HC-12, and they seem to be a little harder to come by, but I just placed an order for 5 of the HC-12's on Amazon (https://www.amazon.com/gp/product/B01MYTE1XR/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1)

Perhaps I should clarify - these devices will only be used for one day, which is why I wasn't too concerned about going through a few AA and D batteries, as long as they'll survive the duration of the event. I have a couple dozen rechargeable Energizer NiMH AA's rated for 2300 mAh, and the motors I'll be using will be a combination of SG90 and MG995 servos and 28BYJ048 steppers, plus maybe a few small 5V DC motors.

Let's say in total I have one each of the two servos, stepper, and DC motor operating on each remote device, with the above intervals that gives an upper limit of 36 minutes run time. Would it make more sense to go with the SLA gel battery or 6 D cells and a DC-DC buck converter? I assume in either case, this would be in tandem with 4 AA's powering the Arduino and wireless communications through the Nano's Vin?

Nope, NiMH for these ones. I guess I'm not completely terrified of LiPo's, but I'm inexperienced and fearful I'll blow something up.

Not quite enough voltage, in theory. You need 6.5V for Vin, otherwise the Nano will get less than 5V. That said, the Nano will usually run fine on 4.5V for example. For battery projects, it's often better to avoid using Vin, linear regulators are not very efficient, and can easily overheat if to much current is drawn from them. You could use 4x AA NiMH and power the Nano directly to its 5V pin. Just don't forget and put non-rechargeables in because 6V connected to 5V pin could damage the Nano.

If I resolve to use 4 NiMH AA's at 1.2V on the 5V pin, I'd then need a solution to power the motors separately. In that case, would the 7.2V NiMH RC batteries with a buck step down be an appropriate solution? The two I have now are 3600 mAh, and I suspect the combination of servos and steppers I'd be using on any given remote unit would be sufficiently covered by this capacity, again by way of relatively short duration run times over the 8 hours of the event.