How you connect depends on what your appliances are. Some things need 120 volts alternating current. Some things need 12 volts direct current. USB things get 5 volts direct current. Some things need to have power when the sun is shining. Some things need power when it is dark.
Make a list of all the things you want to supply power to identifying what kind of power and how long you want them to work. To have power for night and rainy days you need a battery. The size battery you need depends on your list and your wallet.
With a 12 volt DC battery and an inverter you make 120 volts AC. The size depends on the appliances. You probably don't want to buy enough inverter to run everything at once. Go back to your list and figure out the maximum at once requirement.
The inverter has losses. If you have a choice to power something direct from the battery or from an inverter, use the battery. Each conversion will likely waste 20%. A 12 volt fridge with a 120 volt adapter running from a 120 volt inverter will waste 20% converting 12 to 120 then another waste from 120 back to 12 to run the fridge.
A Goal Zero Yeti 400 is a 400 watt hour battery, a 10 amp solar charge controller, and a 300 watt inverter in a handy case. My electric shaver is only 3 watts so my old 100 watt cigarette lighter plug inverter is plenty. The Goal Zero Yeti 400 technical specification says that the battery is 33 amp hours, 396 watt hours. Amazon sells wheelchair batteries that size for $75. There are some savings available. The goal zero charging port can only take 10 amps, about 200 watts of solar. A solar charge controller from Amazon can be bought for $11.
Amazon sells cigarette lighter sockets and USB charger sockets that can connect direct to your battery. Then you plug those in. Amazon sells inverters that also connect directly to a battery. With 300 watts of solar you really want a battery much bigger than a tiny wheelchair battery or a Yeti 400.