Open the avast virus chest and select the files you want, right click and select delete.
The PUP or rather MyWebsearch, is a toolbar commonly installed as a result of either thinking it would benefit you (rather than the makers) or as an add-on with an application/utility you installed.
How to stop it happening again, don't take things at face value if offered a toolbar/application that is going to improve your life/searches, etc. ask yourself why they would offer this for free and do some searches on the product/toolbar. When installing applications, watch the screens as they are displayed, check what is checked/ticked by default and do you want it.
Personally ccleaner is fine, it has a registry cleaner that isn't too aggressive so is a little safer than some others, but all registry cleaners can impact on your system. Many of the registry cleaners have settings to backup the changes so that they can be reversed. But you would have to first bump into a problem and understand that it is a registry problem and then which registry backup to restore.
When using registry cleaners you really need to know a bit about the registry to understand what it is offering to remove and how that may impact on your system, most people haven't got that experience, so they are trusting blindly in the application.
So hopefully you are getting the general idea that messing with the registry can seriously impact on your system.