A clean install is a good thing, but... reinstalling is a pain. You can just do a simple copy and paste and it will probably work.
The mods file has your mods and package forms of cc. So you only put that in the sims 3 folder you want cc in.
The world files install to worldcaches as well as dcCaches and the InstalledWorlds folder.
Venues and Sims create library files, so anything you can find in your bins are in library files as well.
If you saved an outfit or a sim in CAS, then that file goes into the respective folder as well.
And, of course, any saves drop into the saves folder.
Usually, you generate a new sims 3 folder and you copy over the DCcache folder for most of you installed stuff (through the launcher).
The backups aren't important except for cc stuff you want to transfer with your uploads - so patterns!
The world file needs to be there to show as an option when you want to play there. So, I think that is why it installs into extra folders as well.
It really is a copy and paste event as long as you know what you want to bring over.
I would NOT go into purchase history myself. It takes forever to load and it times out. Just use the regular store pages and follow my install guide. The spreadsheet I uploaded has every link provided and keeps you from dup installing.
Ask me any questions and I'll try not to tell you too much and confuse you.