Like the other guys above said, I think just poking around the forums will be a good start. It would be hard to say "this need comes up in all productions" and try to build a tool or process around that to showcase your skills. Each production is different and the needs are constantly changing. Pipeline tools have to be adaptive and modular to production. Building a library of modules that handle such things moving/interpreting/extracting at the high level such as files and folders to such things that are at the micro level like scene data (joints, meshes, points and deformers).
I'd say from a high level, most if not all productions connect to some repository such as Perforce. When I started at my job there was no convenient way for artists to connect and manage their Maya scenes with Perforce. This was a manual thing for them but now they can checkout/revert/check status/submit all within Maya. So my advice would be to download Perforce (it's free). There are free online hosting sites for Perforce too. So from a Pipeline standpoint, I'd become very familiar with Perforce and the commands.
Now I've just begun to help with getting our Substance Designer suite to play nice in our production and it's been challenging to work with so that could also be a good place to start.
Artist accessing tools is another thing that comes up often. Shelves work great for tools but as production grows, the number of tools do as well. The number of tabs and tools that get thrown up there can get out of control quickly. Users and Artists are particular on how they want to access tools. Some prefer Shelves and some prefer menus. We've settled with a Tool Suite that is doc-able. The suite is modular and can expand easily as production needs grow.
So the take away here I guess is I'd begin your exploration at a high level. Artist want quick access to tools and these tools need to aid in their workflow. Pipelines that allow for quick access to data, allow to iterate fast and help them manage this data for them is one of the most important aspects of a smooth running pipeline.
Just my $0.02. Hope that helps some. It is a vague topic only because it cover such a wide range of needs for a production.