bigpup's post here is the one to go with, if, as you say, you'd prefer to run both 32 and 64 bit programs.
Remove any residual Wine related items and try again, though this time, make sure both the devx and 32compat libs are loaded beforehand. You must then run (all lowercase now) "ldconfig" from within a terminal and let the prompt return before running winecfg.
When asked about Gecko or Mono, hit the radio button for download. If it doesn't auto-start within a few seconds, Ctrl+C to close the Wine dialog and rerun winecfg.
As for the package from QuickPet, you could download the pet on its own and convert it to a loadable "squash," or SFS package.
If you'd like to take this route and avoid installing the pet, ask -- the method is easy.