<em>Automate the Boring Stuff with Python</em> by Al Sweigart and <em>Python Playground: Geeky Projects for the Curious Programmer</em> by Mahesh Venkitachalam are two good choices to start with.
They both use project-based approaches to learning Python and getting practice.
I'd suggest starting with Automate the Boring Stuff because it's intended to be more beginner-friendly than Python Playground. Then once you complete the first book, move on to the second.
Using those two in tandem should give you a good stream of projects to work on to become more familiar with Python.
Not many people think 'Learn Python the Hard Way' is a good website (not sure about the book) to learn python. I would defenitly recommend 'Automate the boring stuff' over it (it's free anyway so might aswell take a look). There's defenitly intermediate stuff to gather for it. It has a nice overview of the content and defnitly contains a lot more information than LPTHW. Also has a nice overview of some popular libraries.
Later chapters contain web scraping, excel spreadsheets, pdf/word docs, csv/json, sending emails. So might be interesting enough.
If you want some more 'advanced' projects I would maybe recommend 'Python playground: geeky projects for the curious programmer', wich is from the same publisher as 'Automate the boring stuff'
this site apperantly also has some free python books wich might interest you