An Uno has plenty of processing power for what you need, but depending on the interface for the components you attach (LCD, RTC, barometer, humidity) you may find that you're short of pins - a Mega may be easier.
You may have an issue with the length of wire runs from your sensors impacting your readings - you'll be analogReading for temps and wind direction - how far from the arduino will they be?
If you want an SD card, maybe consider an ethernet shield (which has one) and then the arduino can also send weather data to the PC directly rather than having to remember to take the SD card over there periodically.
I'd suggest you start small - work on one sensor at a time and figure out how to read it. An Uno might be nice for this task - cheaper to replace if you destroy it and useful for subsequent projects if you don't.
One thing to design up front though is the display; you'll need the rendering of your data elements figured out so you can decide how large an LCD you need.