Not a tall order at all....
You can get all of that from Ecowitt (The Misol branded unit you mentioned is just a 3rd party branded Ecowitt/Fine Offset sensor)
Check out the Ecowitt website at
www.ecowitt.com and also the Ambient/Ecowitt forum on this site
You can get a HP2551 console or go headless with a GW1000 and any combination of sensors to your hearts desire!
These both can upload to the usual internet weather sites including Ecowitt own excellent Internet service. As a bonus you can also send to a custom server location which would suite if you have a linux database running somewhere.
If thats challenging then yes you can go the RaspPi route (many free weather software database solutions exist) and some of these offer a full Pi/Software image so there would be a minimum of understanding needed (CumulusMX etc).
Plenty of help available on these forums if you dont understand or want more pointers!