Well I have been researching this myself as I have a couple of the 24 volt panels to use.
There are so many things to consider, so I am going to hit a couple of them.
How long will you want the battery to last without solar. You will need to calculate your amps needed and use this to size your batteries. When using batteries, you should never discharge them more than 50 percent.
Now you need to figure out how long it will take your panel to recharge the battery. You can figure no more than 6 hours of peak sun per day, and if your not pointing the solar panels through the day, you can cut that down an hour to 5 hours or less.
Now the charge controller. There are PWM and MPPT charge controllers. You will get only about 60 to 80 percent effiency from the PWM controller. These are the cheaper controllers. You will get 90 percent plus out of an MPPT and you can mix voltages.
The challenge is that with a 24 volt panel and a 12 volt battery bank, you will have an issue. If you use a PWM charge controller to convert from 24 volt to output 12 volts, you will take a huge power loss of about half.
The MPPT can easily adapt from the 24 volt panel to 12 volts. These controllers are more expensive.
With what you have outlined you can get buy with a lower amperage MPPT charge controller. Probably a 20 amp. I am looking at this one.
https://www.amazon.com/dp/B00ZV3I3UU/ref=psdc_2236627011_t2_B07429RK43?th=1But I will be getting a higher amperage model.
Now about inverters. If your battery is close to your gear, you can run 12 volts without issue. This assumes you can get a charger for your laptop.
If you are only charging the laptop, and maybe a couple of house lights, or even LED Christmas lights, I would get a small 80 watt power inverter from Harborfreight for $20.00.
I had an electrical guy go over the difference between the modified sine wave and the pure sine wave inverters. He believed that you should try the cheaper modified sine wave inverter. If it doesn't cause you a problem, stick with the cheaper ones. His point is that its only critical for very specific electric motors and even your refigerator can run on modified sine wave.
Little more on batteries. Your cheapest will be Lead Acid batteries. A marine battery will give you about 112 amp hours. Two 6 watt golf cart batteries will give you over 200 amp hours.
Lithium batteries will last longer, but they are much more expensive.
I suggest listening to the pod casts done by Steven Harris. Solar1234.com, (Look for the chicken coop audio pod cast), battery1234.com has several pod casts on choosing batteries and building battery banks.
Good luck.