don't get CWM and RM mixed up - they are separate. RM is just an app that facilitates the use of dl and installing roms. but, CWM is an actual recovery, just like SPR. some people prefer one over the other, but i've never had any problems with either.
that being said, you are actually in recovery. to get the newly dl'd zip to your sdcard, go to "partitions menu", then "mount USB storage". this is the same as mounting your sdcard when phone is on. from there, just drop the zip file from pc onto root of sdcard. then select "unmount", and use the power button to toggle back to the main menu screen.
from there, it's the same process: wipe data, wipe cache, install zip.