For simplicity and ease + frugality, I would suggest maybe looking at a smaller "All in One" system, with Solar Controller & Inverter combined like an MPP type of unit; General listing here:
https://usa-mpp-solar.com/store-buy-now
Solar Panels can be had cheap if your open to used panels. Check out
https://store.santansolar.com/product-category/solar-panels/ but there are other vendors in various places in the US and even some on EBay... Many here have bought from SantanSolar and are tickled pink with their purchase.
Batteries: Simply put, any Lead Variant is only 50% useable, so for example if a Battery says it's 100AH, you can only use 50% of that before damage to the battery happens. Vehicle batteries are useless in Solar Applications, you need to use Deep Cycle Lead batteries which includes deep cycle marine, golf cart and "some" RV batteries. Craig's math is bang on the button, so you'd be looking for 12 Volts an 500Ah to have enough useable. Lead is fairly temperature tolerant so they work in below freezing temps as long as they are properly charged & maintained (see ref doc link below). If you decide on Lead, then stick to Real Deep Cycle batteries made by Trojan, Rolls Surette, Deca and so on, stay away from knock offs and off brand labels. Unfortunately even brands like Exide have gone really crappy in the last couple of years and "store brands" are the worst out there.
Excellent article on Care & Feeding of Lead Acid Batteries:
https://www.solacity.com/lead-acid-battery-care/
Many people looking to heat water for Chicken Coops often look at a Solar Water Heating system which can be done cheaply with a little DIY creativity and a pinch of ingenuity. Check this site out, many plans and practical applications, a terrific resource:
https://www.builditsolar.com/Projects/WaterHeating/water_heating.htm
Hope that helps, Good Luck
Steve