@DLane is describing Ambient Weather WS-1400-IP, not Acurite (easy mistake to make ).
Acurite uses something similar to Observer IP, they call theirs SmartHub, and not every model comes with one (see my original reply in this thread). This little adapter connects to the wired Ethernet and to the Acurite 5-in-1 sensor, which by itself can’t connect to the internet/wifi.
5-in-1 family of sensors does not come with rechargeable batteries, and @jangell2 is right that solar panels only power the fan to keep temperature closer to ambient. They actually advise against rechargeable batteries, because they are supposedly can’t work well at low temperatures. Personally I think they simply didn’t want to deal with sharper voltage drop when the rechargeable batteries are low on power.
My batteries have worked well so far (haven’t had to replace them yet), but because they are not rechargeable by the sensor, I would advise against installing the sensor high up (somewhere not easily serviceable).
Personally I have mine mounted on a fence, about 6ft off the ground. In order to have an accurate wind and rain measurements, you should try providing as much clearance above the sensor as possible, so do not install it right next to the wall and be careful if installing it on the roof.
My Acurite unit came with 5-in-1, HD display and SmartHub, setup similar to the first version you posted. HD display is rarely used, I mostly use apps on my phone.