I want to use my old netbook for a few very simple purposes, mainly accounting - spreadsheet documents and going online to get numbers. I have another computer for gaming, movies and all other bell and whistle programs. I want the netbook system as clean and streamlined as possible. So I returned my netbook to factory settings, which unfortunately came with a ton of windows based bloatware. If I do a complete install of ubuntu as the sole OS, will it actually wipe out these unwanted programs (e.g. norton antivirus trial)? If not, can I uninstall them after I install ubuntu, or do I need to wipe them out beforehand?
Removing Windows will delete ALL Windows software. So that is a firm YES to your question.
You can wipe your whole disc (and all Windows related items) during the installation of Ubuntu so need to do anything special upfront or after installing. At some point it will ask what to do with the disc lay-out (ie. partitioning). If you choose "wipe disc" it will do this for you (you can do it also with the "something else" option but that would require for you to have some understanding on how to manually alter your partitions. Might be a bit overwhelming for a new user).
Installing Ubuntu as the sole OS (taking the whole hard disc volume) will wipe out everything there is inside the disc. Ubuntu will install its own applications. As you mention, the machine you have is a netbook so my recommendation is to install Lubuntu as the OS, because it's lighter and will run better on your machine.