Welcome to the forum!
Did you flash the GAPPS package after flashing the JB ROM? If you did not, you will not have the Play Store.
Does your version of CWM see a microSD card?
If so, grab whatever ROM you want (ICS or Jelly Bean) and flash it, along with any other required packages (GAPPS, kernels, etc) and put them on the microSD.
Boot to CWM, wipe Cache, wipe Davlik Cache. Try a full wipe (it will not wipe the internal /data/media/).
Install the zips.
If you do NOT have access to your microSD from CWM, then I would suggest this:
Boot to CWM
Wipe Cache
Wipe Davlik Cache (in advanced)
Install zip from SD card
Choose the JellyBean AOSP and install it
Choose the GAPPS package (if you downloaded it). If not, just boot without it.
Boot up.
Download the ROM you want and save it on the internal memory.
Boot to CWM, flash the ROM you want.