After unlocking the boot loader, this is what I would do:
Get the SD card and format it. Use the SD formatter 4.0 application (official tool from the SD consortium to format SD cards, google the name) and always switch on the format size adjustment option. Never format an SD card with Windows or Linux for using it in phones, cameras, Wii, etc. Always use this tool or the device itself for formatting. If you don't have a SD card reader, connect the phone with the SD card inside to the PC and select the Disk drive option for mounting the card.
Step 2 - Install recovery
2.1) As you said, get the CWM recovery from the official site. If you are from Birmingham, you need the GSM version (the one that is not CDMA, which is primarily for USA). Beware, if you install the wrong version, you will brick your device.
2.2) Install it. You have a few options: a) follow one of the methods explained in post [TUTORIAL][ROOT] Root Tutorial + CyanogenMod 10 for the Wildfire S (marvel) (sorry, I can not post links), b) you can use the tool I mentioned a few posts ago HTC Wildfire S All-In-One Toolkit (advantage: really easy and you will not need to deal with the command line, disadvantages: ads and you will not learn how to use command line ).
2.3) As your phone did a factory reset when the unlocking was performed, it will be advisable to completely clean it now before finishing. Do the four wipes:
HBoot->Recovery->wipe cache partition, wipe data
HBoot->Recovery->Advanced: wipe battery stats, wipe dalvik cache
2.4) Make a backup (usually called NANDroid) of your cleaned factory reset phone. HBoot->Recovery->Backup. The backup may take a while and it will use around 300MB.
Step 3 - Install SuperSU
3.2) Get the file SuperSU.zip from a XDA thread and copy the file to your SD card. Search for a thread called [Root App] Superuser v3.1.3 Final & SuperSU V0.93 latest Flashable Zip. July 13, 2012, but do not install both apps, it is one or the other. I have installed and used SuperSU, and it is working properly.
3.3) HBoot->Recovery->Install zip file from SD card (search for SuperSu.zip).
3.4) Your phone is now rooted. In your description you were trying to do twice the same with root.zip and SuperSU.zip, and that is wrong as far as I know.
Optional Step 4 - Backup
4.1) IMHO, I would backup at this point, where the process has finished, and move the previous backup (point 2.4) to the PC just in case I would need it.
4.2) Reboot, and enjoy being root .
Once you are here, come again and we can discuss about getting rid of the unwanted apps (there is more than one option).
I hope this helps you. Regards.