Here. Read this basic primer on a basic system.
Building a vehicle mounted solar power system? Let me help.
www.mobile-solarpower.com
Redarc is good, but very expensive.
Batteries are almost a commodity now. That same site I just gave, Will Prowse, tears down and reviews Batteries all the time, and he gives a list of recommended components for your build that he has tested and tore down.
I would avoid renogy, though their Batteries aren't bad, but you can get a good LiTime or Redodo 100Ah 12.8v LiFePO4 12v for $230 or less.
There are thousands of threads on 2nd battery mobile overland builds. Don't start picking your components before you have a complete design, wiring diagram, and MOST IMPORTANTLY you have filled out an energy audit with all the actual no-guesswork loads you will run.
If all you use 120v for is tool Batteries, a 600W inverter is fine but too weak for much else.
Lights are LED and are 12-24v dc, not ac.
Fridges are 12-24v dc, not ac. The fact you listed them as ac loads, tells me you haven't actually spent any time at all looking at your actual loads and usage. That's like asking people to comment on " need transportation, maybe bicycle, maybe Ram 2500, what do you think?" Its just a waste of everyone's time to get specific yet.
So, go over to that link to Will Prowse's DIYmobilesolar I gave you, then read his basics links. Then maybe watch his YouTube basics series. And you won't get better parts recommended than his probably.
In general, Victron are the best "just work right" parts, expensive. Renogy are the cheapest, and break a lot, lot of issues posted, zero customer service.
Parts needed-- these all come as standalone, or as various 2 or 3 fuction combos. Standalone easier to replace or fix, maybe more space and cost.
Power sources--
1.Dc dc charger from starter battery/alternator.
2. Solar, need an mppt solar charge controller, SCC. Specs depend on system.
2A. Solar panels, specs depend on system, amount depends on your energy audit and fit
3. Ac batterycharging, need a good ac charger that does right 3 or 4 step voltages at right amps for your batteries.
Storage--
1. LIFEPO4 12V batteries. Low temp charge protection maybe, heated maybe, depends on your use.
AC 120v inverter--
Sized depending on your ac loads, how much parasitic piwer it wastes, and what your battery setup can support for amps flow. Can also get ac charger/inverter combos.
400W-- toy for charging cordless batteries.
600W same
1000W-- min for most truck camping setups. Can do small elec kettle, or an INVERTER MICROWAVE ( not normal one, but better power use and $119 or so)
1500W-- min for running normal size electric kettle or small microwave, some weak induction burners etc.
You can get pretty inexpensive if all you actually need is to charge battery packs. And renogy makes a combo ac charger, dcdc charger, solar mppt scc, if you want low cost and can risk all sources breaking at once.
Good luck, hope that helps, come post more when you can give better system needs.