I'm really a solar-power beginner, though I've tinkered with it off-and-on for years. Definitely take what I have to say with a grain of salt!
I see that you understand that you will need more energy production to power the heavier loads that you have listed. I don't have a lot of knowledge regarding inverters but I did want to maybe emphasize your actual question...which is
"What is the most powerful modified sound sine wave power inverter for under $100 bucks to get me started?". Now having re-stated that...
The ratio of pv panel to battery storage is kind of reversed in my mind. I think I would invest, to begin with, in more pv panel power (three more would be great!). As it is, you can't use but probably a little over 20 amp hours on good sunny days being as your panel can only produce that much power and there are inherent system-losses. Your battery bank is capable of being discharged down to 50% state-of-charge, which would be 65aH of power usage (half of 130aH) without over-discharging it. But, your single pv panel cannot restore that much power to the battery bank. You have the capacity to store 65 amp hours daily but only capability of refilling only 20 amp hours each day. If you use more power than the pv panel can provide then in a few days you find your battery bank over-discharged and maybe even dead...not good for the batteries.
Do you already have a solar charge controller? Amp capacity (30amp would be great!)? PWM or MPPT? A PWM controller is around 70% efficient while a MPPT will be around 90-95% efficient. This matters more for multiple panel setups...but, to future proof things the MPPT would be best. If you don't have a charge controller yet I would say add the inverter funds to the charge controller funds and go with an MPPT. If you've already bought a PWM then continue on with what you have, maybe later upgrading to an MPPT. ?
Inverters will be around 80% efficient...so roughly, to power a 100w a/c item you need 120w going into the inverter. And, as long as the inverter is powered on it will draw power from the battery bank whether a load is being powered or not. A cooler with two or three 2-liter drink bottles
Both heating and cooling are power-suckers.
I would optimize my solar setup's ability to refill the maximum power the battery bank can provide before I ventured on to other things.
Here are some *very, very* rough load calculations that I made (and I probably have errors in them, but I think they're close):
*2 amp hours - two 6w bulbs - 4 hours each, per day
**53 amp hours - two 15w fans for chicken coop - 24-hours a day (running only one will get you close to your daily production limit)
**67 amp hours - 60w waterer warmer - 12 hours per day (trimming the time to maybe 8 hours might work in regards to power, but freezing?)
***35 amp hours - rough guesstimate for 8 hours of mini-fridge cycling per day
Notes:
*To save a couple of amp hours you could cut this down to one bulb
**The fan and water heater will not be running at the same time, so that's a plus.
***The min-fridge should self-cycle on/off...running roughly 1/3 of the time...in the winter probably less...in really hot weather, possibly more.
Also, any a/c item running through the inverter will involve the 20% rough overhead of power requirement.
These are just some thoughts from somebody who knows just enough to be dangerous...seriously. I hope somebody comes along and corrects me on errors, as this is a learning experience for me and mental(illness) exercise. So take the above with a grain of salt...it's worth exactly what you paid for it!
