Replicate papers (beginner)
Bioinformatics is a big and very heterogeneous field with a lot of variation, so it's hard to recommend something that covers everything. That said, I think the best you'll do is to build familiarity with some of the common tools with some canned analyses. 

One possible option would be some of the scRNA-seq workflows from the Pachter group, they seem to be fairly conscientious about documentation. Here is one such canned analysis, here is the paper, here is a blog post about it that suggests next steps and discusses at a high level. 

scRNA-seq is just what's been trendy for a few years, next year it will be something different. But it at least gets you familiar with some of the file formats and concepts such as alignment, etc.

Hope that helps.